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.

MSC: 54H15, 57S99

Pages:  110$-$119     

Volume  70 ,  Issue  2 ,  2018