Menger probabilistic normed space is a category topological vector space

Abstract

In this paper, we formalize the Menger probabilistic normed space as a category in which its objects are the Menger probabilistic normed spaces and its morphisms are fuzzy continuous operators. Then, we show that the category of probabilistic normed spaces is isomorphicly a subcategory of the category of topological vector spaces. So, we can easily apply the results of topological vector spaces in probabilistic normed spaces.

Keywords

• Category of probabilistic normed space
• Category of topological vector space
• Fuzzy continuous operator