Balls as subspaces of homogeneous type: on a construction due to R. Macias and C. Segovia

AIMAR HUGO

Recent Developments in Real And Harmonic

Birkhauser

Año: 2008

                 In this chapter we give an equivalent point of view for quasi-metricstructures on a set X in terms of families of neighborhoods of the diagonal inChapter XXX. We use this approach and the iterative process introduced by R.Mac ́ and C. Segovia in ‘A well behaved quasi-distance for spaces of homogeneous     ıastype ́(Trabajos de Matem ́tica, IAM, 32, 1981, 1–18) in order to show that the balls                         ain the new quasi-distance have a specific regularity at the boundary.