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The Operators' Theorems on Fuzzy Topological Spaces

Journal: Sahand Communications in Mathematical Analysis (Vol.19, No. 1)

Publication Date:

Authors : ; ; ;

Page : 57-76

Keywords : Fuzzy norm; Fuzzy topology; Fuzzy boundedness; Fuzzy continuity;

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Three types of fuzzy topologies defined on fuzzy normed linear spaces are considered in this paper. First, the relationship between fuzzy continuity of linear operators and fuzzy boundedness is investigated. The uniform boundedness theorem is then discussed, so too is the norm of a linear operator. Finally, the open mapping theorem is proved for each of the three defined fuzzy topologies, and the closed graph theorem is studied.

Last modified: 2022-07-31 17:26:09