Soft Vector Spaces and Soft Topological Vector Spaces

Abstract

Molodtsov introduced the concept of soft set theory, which can be used as a generic mathematical tool for dealing with uncertainty. In fact, it is free from the difficulties that have troubled the usual theoretical approaches. Roy and Samanta [13, 14, 15] defined several basic notions on soft set and studied many properties. In continuation of [13, 14, 15], here we have introduced soft topological vector space and studied few basic properties related to soft topological vector spaces. For introduction of soft topological vector space, there is need to define soft vector space and soft product topological space, which has been encountered in this paper.

Key words and phrases. Soft set, vector sum and scalar multiplication of soft sets, soft vector space, soft product topology, soft topological vector space.

1991 Mathematics Subject Classification. 62C86, 57N17, 15A03