Retractos uniformes equivariantes

Ponente(s): Luis Augusto Martínez Sánchez, Sergey Antonyan

The purpose of this talk is to present some of the most important results we have obtained in [1]. The aim of this work is to develop an equivariant theory of uniform absolute neighborhood retracts or UANRs. In most of our results the acting group G is compact and Hausdorff. We extend the notions of uniform ARs and uniform ANRs to the class of metric G-spaces equipped with invariant metrics. Accordingly, the concepts of G-UARs and G-UANRs are introduced. Similarly, we define and study the notions of G-UAEs and G-UANEs, which are generalizations of uniform AEs and uniform ANEs, respectively. We are establishing equivariant counterparts of some important results from Sakai’s book, as well as, from the papers by M. Kurihara and Yaguchi. [1] S. Antonyan, L. A. Martínez-Sánchez, Equivariant uniform absolute neighborhood retracts, submitted.