A Note on Strongly Lower Semi-Continuous Functions and the Induced Fuzzy Topological Space Generated by Them
Keywords:Topology, fuzzy topological space, SLSC function, regular F(sigma)-subset, s-induced fuzzy topological space.
AbstractA new class of functions called strongly lower semi-continuous (SLSC) functions is defined and its properties are studied. It is shown that the arbitrary supremum and finite infimum of SLSC functions are again SLSC. Using these functions, an induced fuzzy topological space, called s-induced fuzzy topological space on a topological space (X, T), is introduced. Moreover, some incorrect results on fuzzy topological spaces obtained previously by some authors are identified and modified accordingly. Examples of the newly defined induced space are given and their various properties are investigated. Interrelationships between a fuzzy topological space (X, F) and the s-induced fuzzy topological space generated by the crisp members of F are examined. In this process, different lower semi-continuities and induced fuzzy spaces generated by them have been defined in a general set up and their few properties have been studied.
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