On strongly α-topological vector spaces

Abstract

This paper is devoted to introduce a new kind of topological vector spaces called strongly α-topological vector space and study their relationship with other types of topological vector spaces. The α-bounded and totally α-bounded sets are defined by using α-open in strongly α-topological vector space and some of their characterizations are established.

Subject Classification: [2010]:

• 57N17
• 57N99

Keywords:

• Open set
• α-open set
• Strongly α-topological vector space
• Strongly α-irresolute function