Fixed Point Set and Equivariant Map of a S-Topological Transformation Group

Abstract

The fixed point set and equivariant map of a S-topological transformation group is explored in this work. For any subset K of G, it is established that the fixed point set XK is clopen in X and for a free S-topological transformation group, it is proved that the fixed point set of K is equal to the fixed point set of closure and interior of the subgroup of G generated by K. Subsequently, it is proved that the map between STCG(X) and STCG’(X’) is a homomorphism under a Φ’- equivariant map. Also, it is proved that there is an isomorphism between the quotient topological groups and some basic properties of fixed point set of a S-topological transformation group are studied.