s-topological Groups and Related Structures

Abstract

s-topological Groups and Related Structures In this research work, we study the classes of s-topological groups, Irr-topological groups, irresolute topological groups and a wider class of S-topological groups which are defined by using semi open sets and semi continuity introduced by N. Levine. It is shown that s-topological groups, S− topological groups and Irrtopological groups form a generalization of topological groups, where as irresolute topological group is independent of topological groups and that they are different from several distinct notions of semi topological groups which appear in the literature. Counter examples are given to strengthen these concepts. Some important results and applications of these topologized groups are presented. Similarities and differences from topological groups are investigated. s−regularity and s−compactness have been studied for s−topological groups. Relation between topologized groups has been established. Semi quotient mappings which are stronger than semi continuous mappings have been defined and then semi quotient spaces and groups are studied. It is proved that for some classes of s- topological groups (G,∗,τ) the semi quotient space G/H is regular.