Topological stability for fuzzy expansive maps

Abstract

We introduce the definitions of expansivity and topological stability for homeomorphisms on fuzzy metric spaces. We show some basic properties of fuzzy expansive homeomorphisms. Moreover we prove Walters's theorem in the context of fuzzy metric spaces, i.e., a fuzzy expansive system with the fuzzy shadowing property is fuzzy topologically stable. © 2020 Elsevier B.V.The authors would like to thank Carlos A. Morales, for useful talks on the subject of expansiveness and shadowing. Also, the authors would like to thank Professor H. Miranda and the anonymous reviewers for their valuable comments that helped to improve the final version of the article. The first author was partially supported by CONICYT PFCHA/DOCTORADO NACIONAL/2017-21170110 and Agencia Nacional de Investigaci?n y Desarrollo-ANID, Chile, project FONDECYT 1181061. The second author was partially supported by Agencia Nacional de Investigaci?n y Desarrollo-ANID, Chile, project FONDECYT 1181061, by Universidad del B?o-B?o, Chile, project 196108 GI/C, and by Programa do Postdoutorado Ver?o 2017-2019, IMPA, Rio de Janeiro, Brasil. The last author was partially supported by FONDECYT (Per?) contract 100?2018