Menger probabilistic normed space is a category topological vector space
Journal: Sahand Communications in Mathematical Analysis (Vol.3, No. 2)Publication Date: 2016-06-10
Authors : Ildar Sadeqi; Farnaz Yaqub Azari;
Page : 25-32
Keywords : Category of probabilistic normed space; Category of topological vector space; Fuzzy continuous operator;
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.
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