On fuzzy semiregularization, separation properties and mappings (Q1187872)

A new definition for fuzzy \(\delta\)-open and \(\delta\)-closed sets is supplied in this paper and it has been shown that the topology \(\tau^ \delta_ X\) generated by fuzzy \(\delta\)-open sets is precisely the fuzzy semiregularization topology \(\tau_ S\); in studying the basic properties of \(\tau^ \delta_ X\) and \(\tau_ S\), it has been shown that unlike general topology fuzzy semiregularization is not preserved for Tychonoff products. Some fundamental separation properties are studied along with the relationship between \(\tau^ \delta_ X\) and \(\tau_ X\) in the context of these axioms. In fuzzy setting the author has studied compactness and connectedness by means of fuzzy semiregularization topologies. Finally, super-continuity has been defined, some characterizations are given and a comparison between different forms of continuity in fuzzy topology has been studied.