Groups of generalized isotopies and generalized G-spaces

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.