Soft Topological Vector Spaces in the View of Soft Filters
Global Journal of Pure and Applied Mathematics. ISSN 0973-1768 Volume 13, Number 7 (2017), pp. 4075--4085 © Research India Publications http://www.ripublication.com/gjpam.htm Soft topological vector spaces in the view of soft filters M. Sheik John Department of Mathematics, NGM College, Pollachi-642 001, TamilNadu, India. M. Suraiya Begum Research Scholar, Department of Mathematics, NGM College, Pollachi-642 001, TamilNadu, India. Abstract In our present work, we have introduced the concept of soft topological vector spaces in the view of soft filters. We also discuss some of the properties of soft filters in soft topological vector spaces. AMS subject classification: 03E72, 54A40. Keywords: Soft open set, Soft topological space, Soft topological vector space, Soft balanced neighborhood, Soft filter. 1. Introduction Classical tools of Mathematics [26] cannot solve the problems which are vague rather than precise. To overcome these difficulties Molodtsov [16] initiated the concept of soft set theory which doesn’t require the specification of parameters. He applied soft set theory successfully in smoothness of functions, game theory, operation research and so on. Thereafter so many research works [3] [5] have been done on this concept in different disciplines of Mathematics. Research on soft sets based decision making has received much attention in recent years. Later, in 2003, Maji et al. [14] [15] made a theoretical study on soft set theory. They introduced several operations on soft sets and applied soft sets to decision making problems. In 2007, Aktas and Cagman [1] introduced a basic version of soft group theory, which extends the notion of a group to include the 2 M.
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