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

Abstract

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 in X×X.We use this approach and the iterative process introduced by R. Macías and C.Segovia in.A well behaved quasi-distance for spaces of homogeneous type (Trabajosde Matemática, IAM, 32, 1981, 1?18) in order to show that the balls in the newquasi-distance have a specific regularity at the boundary.