Balls and quasi-metrics: A space of homogeneous type modeling the real analysis related to the Monge-Ampère equation

We prove that having a quasi-metric on a given set X is essentially equivalent to have a family of subsets S(x, r) of X for which y∈S(x, r) implies both S(y, r)⊂S(x, Kr) and S(x, r)⊂S(y, Kr) for some constant K. As an application, starting from the Monge-Ampère setting introduced in [3], we get a space of homogeneous type modeling the real analysis for such an equation. Acknowledgements and Notes. Supported by Programa Especial de Matemática Aplicada (CONICET) and Prog. CAI+D, UNL. Programa Especial de Matemática Aplicada (CONICET), Dpto. de Matemática, FIQ. UNL. Programa Especial de Matemática Aplicada (CONICET), Dpto. de Matemática, FIQ. UNL. Programa Especial de Matemática-Aplicada (CONICET), Dpto. de Matemática, FCEF-QyN, UNRC.