EMIS ELibM Electronic Journals
Vol. 70, No. 2, pp. 110–119 (2018)

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Groups of generalized isotopies and generalized $G$-spaces

P.S. Gevorgyan and S.D. Iliadis

Moscow State Pedagogical University, Russia E-mail: pgev@yandex.ru and Moscow State University, Russia E-mail: s.d.iliadis@gmail.com

Abstract: The group of generalized isotopies of topological space is studied. A relationship of this group with the group of homeomorphisms is established in case of locally compact and locally connected space. Notions of generalized $G$-spaces and there equivariant maps are introduced. It is proved that a new category of generalized $G$-spaces is a natural extension of the category of $G$-spaces.

Keywords: Compact-open topology; group of homeomorphisms; isotopy; group of generalized isotopies; generalized $G$-space.

Classification (MSC2000): 54H15; 57S99

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Electronic fulltext finalized on: 13 Mar 2018. This page was last modified: 25 Sep 2018.

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