s-Topological vector spaces

Abstract

In this paper, we have de ned and studied a generalized form of topological vector spaces called s-topological vector spaces. s-topological vector spaces are de ned by using semi-open sets and semi-continuity in the sense of Levine. Along with other results, it is proved that every s-topological vector space is generalized homogeneous space. Every open subspace of an s-topological vector space is an s-topological vector space. A homomorphism between s-topological vector spaces is semi-continuous if it is s-continuous at the identity.