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.
