On G-Expansive Homeomorphisms and Generators

Abstract

In this paper, we define the notion of a G-generator for a homeomorphism on a compact G-space and characterize G-expansive homeomorphism on a compact metric G-space in terms of G-generator. We obtain the relation between G-expansiveness of a pseudoequivariant homeomcrphism on a metric G-space X and expansiveness of its induced homeomorphism on the orbit space X/G. We use this relation to prove the non-existence of pseudoequivariant G-expansive homeomorphism on closed unit interval. Finally, we show that a compact metric G-space admitting a pseudoequivariant G-expansive homeomorphism must be of finite dimension when G is finite.