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S – CONVEX SET IN A TOPOLOGICAL VECTOR SPACE
*Neelam Dubey1, Research Scholar, V.K.S. University, Ara, Bihar. Dr. Omprakash Dubey2, Assistant Professor,J.J. College, Ara,Bihar.
Abstract:
In this present article, we explore S-Convex Sets in topological vector spaces, investigating key concepts like closed sets, open sets, set interiors, and the closure property of S-Convex Sets. It establishes that the closure of an S-Convex Set in a topological vector space remains S-Convex, which differs in technique from metric spaces. Neighborhood systems are employed. It presents theorems involving closed sets, set closures under specific conditions, and the interior of sets in topological vector spaces. It demonstrates that the interior of an S-Convex Set in such a space also preserves the S-Convex property. Furthermore, the chapter derives a result related to S-Convex Sets and S-Convex hulls. \r\n