Groups of generalized isotopies and generalized $G$-spaces

P.S. Gevorgyan and S.D. Iliadis

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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