MV-closures of Wajsberg hoops and applications

ABAD MANUEL; CASTAÑO DIEGO; DÍAZ VARELA JOSÉ PATRICIO

ALGEBRA UNIVERSALIS

BIRKHAUSER VERLAG AG

Año: 2010 vol. 64 p. 213 - 230

0002-5240

In this paper we construct, given a Wajsberg hoop A, an MV-algebraA, an MV-algebra MV(A) such that the underlying set A of A is a maximal lter of MV(A) and the quotient MV(A)=A is the two element chain. As an application we provide a topological duality for locally nite Wajsberg hoops based on a previously known duality for locally nite MV-algebras. We also give another duality for k-valued Wajsberg hoops based on a dierent representation of k-valued MV-algebras and show the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. Wajsberg hoops based on a dierent representation of k-valued MV-algebras and show the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. Wajsberg hoops based on a dierent representation of k-valued MV-algebras and show the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. Wajsberg hoops based on a dierent representation of k-valued MV-algebras and show the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. Wajsberg hoops based on a dierent representation of k-valued MV-algebras and show the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. topological duality for locally nite Wajsberg hoops based on a previously known duality for locally nite MV-algebras. We also give another duality for k-valued Wajsberg hoops based on a dierent representation of k-valued MV-algebras and show the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. Wajsberg hoops based on a dierent representation of k-valued MV-algebras and show the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. Wajsberg hoops based on a dierent representation of k-valued MV-algebras and show the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. Wajsberg hoops based on a dierent representation of k-valued MV-algebras and show the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. Wajsberg hoops based on a dierent representation of k-valued MV-algebras and show the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. topological duality for locally nite Wajsberg hoops based on a previously known duality for locally nite MV-algebras. We also give another duality for k-valued Wajsberg hoops based on a dierent representation of k-valued MV-algebras and show the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. Wajsberg hoops based on a dierent representation of k-valued MV-algebras and show the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. Wajsberg hoops based on a dierent representation of k-valued MV-algebras and show the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. Wajsberg hoops based on a dierent representation of k-valued MV-algebras and show the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. Wajsberg hoops based on a dierent representation of k-valued MV-algebras and show the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. topological duality for locally nite Wajsberg hoops based on a previously known duality for locally nite MV-algebras. We also give another duality for k-valued Wajsberg hoops based on a dierent representation of k-valued MV-algebras and show the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. Wajsberg hoops based on a dierent representation of k-valued MV-algebras and show the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. Wajsberg hoops based on a dierent representation of k-valued MV-algebras and show the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. Wajsberg hoops based on a dierent representation of k-valued MV-algebras and show the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. Wajsberg hoops based on a dierent representation of k-valued MV-algebras and show the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. topological duality for locally nite Wajsberg hoops based on a previously known duality for locally nite MV-algebras. We also give another duality for k-valued Wajsberg hoops based on a dierent representation of k-valued MV-algebras and show the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. Wajsberg hoops based on a dierent representation of k-valued MV-algebras and show the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. Wajsberg hoops based on a dierent representation of k-valued MV-algebras and show the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. Wajsberg hoops based on a dierent representation of k-valued MV-algebras and show the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. Wajsberg hoops based on a dierent representation of k-valued MV-algebras and show the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the quotient MV(A)=A is the two element chain. As an application we provide a topological duality for locally nite Wajsberg hoops based on a previously known duality for locally nite MV-algebras. We also give another duality for k-valued Wajsberg hoops based on a dierent representation of k-valued MV-algebras and show the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. Wajsberg hoops based on a dierent representation of k-valued MV-algebras and show the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. Wajsberg hoops based on a dierent representation of k-valued MV-algebras and show the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. Wajsberg hoops based on a dierent representation of k-valued MV-algebras and show the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. Wajsberg hoops based on a dierent representation of k-valued MV-algebras and show the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. topological duality for locally nite Wajsberg hoops based on a previously known duality for locally nite MV-algebras. We also give another duality for k-valued Wajsberg hoops based on a dierent representation of k-valued MV-algebras and show the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. Wajsberg hoops based on a dierent representation of k-valued MV-algebras and show the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. Wajsberg hoops based on a dierent representation of k-valued MV-algebras and show the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops. the relation to the rst duality. We also apply this construction to give a topological representation for free k-valued Wajsbe