TITLE:
On Fuzzy Regularly Closed Filters in Michálek Fuzzy Topological Space
AUTHORS:
Puthenpurackal Ratnakumar Neethu, Bloomy Joseph
KEYWORDS:
Topology, Fuzzy Topology, Michálek’s Fuzzy Topological Space, Fuzzy Closed, Fuzzy Open, Filters
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.14 No.10,
October
29,
2024
ABSTRACT: C.L. Chang’s introduction of fuzzy topology in 1981 opened up new avenues for parallel theories in topology. However, Chang’s work appears to focus more on the topology of fuzzy sets rather than fuzzy topology itself. In 1975, Michálek presented a functional definition of ordinary topology and later developed fuzzy topology as a distinct extension of this idea, setting it apart from Chang’s approach. While there has been significant research on Chang’s fuzzy topology, Michálek’s version has not received as much attention. This paper introduces the concept of fuzzy regularly closed filters, or FRCM filters, within Michálek’s fuzzy topological space and explores some properties of FRCM ultrafilters.