s-Topological vector spaces

Subject Areas : General topology

M. Khan ¹ , S. Azam ² , S. Bosan ³

1 - Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Islamabad, Pakistan
2 - Punjab Education Department, Pakistan
3 - Punjab Education Department, Pakistan

Received: 2015-08-13 Accepted : 2015-11-01 Published : 2015-05-01

Keywords: s-Topological vector space, Semi-open set, semi-closed set, s-continuous mapping, left (right) translation, generalized homeomorphism, generalized homogeneous space, semi-continuous mapping,

Abstract :

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

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