• Gopal Adak

The Stone - Čech compactification βS of a discrete semigroup S is the set of ultrafilters on S on which the binary operation can be extended uniquely making it a compact right topological semigroup. The idempotent elements in βS have some extra ordinary algebraic structures which are applied in combinatorial problems, especially in Ramsey theory. The idempotent elements of βS, which are not in S induced a topology on the group S which are left invariant. In this paper we study subspace topology on a subgroup T of this left invariant topological semigroup and topology induced by idempotent in the Stone - Čech compactification βT. 2010 Mathematics Subject Classification: 54D35, 54D80, 54F05.

Stone - Čech compactification, ultrafilter, compact right topological semigroup, left invariant topology, idempotent.

"Left Invariant Topology on a Subgroup of a Group G Defined by Idempotents of G*", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.9, Issue 10, page no.c442-c447, October-2022, Available :http://www.jetir.org/papers/JETIR2210256.pdf

"Left Invariant Topology on a Subgroup of a Group G Defined by Idempotents of G*", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.9, Issue 10, page no. ppc442-c447, October-2022, Available at : http://www.jetir.org/papers/JETIR2210256.pdf