s-Topological vector spaces

Journal of Linear and Topological Algebra

مقاله 6، دوره 04، شماره 02، مرداد 2015، صفحه 153-158   

نوع مقاله: Research Paper

نویسندگان

M. Khan^{* 1}؛ S. Azam²؛ S. Bosan²

¹Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Islamabad, Pakistan

²Punjab Education Department, Pakistan

چکیده

In this paper, we have defined and studied a generalized form of topological vector spaces 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 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.

کلیدواژه‌ها

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

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