ON FUZZY $\partial^*$ SPACES
Keywords:
fuzzy $G_\delta$-set, fuzzy $F_\sigma$-set, fuzzy nowhere dense set, fuzzy residual set, fuzzy simply* open set, fuzzy hyperconnected space, fuzzy $P$-space, fuzzy weakly Baire space.DOI:
https://doi.org/10.17654/0973421X22009Abstract
In this paper, a new class of fuzzy topological spaces, namely, fuzzy $\partial^*$ spaces, is introduced and studied. It is obtained that fuzzy $G_\delta$-sets are fuzzy somewhere dense sets but not fuzzy simply open sets, and fuzzy $F_\sigma$-sets are fuzzy $c s$ dense sets but not fuzzy dense sets. Fuzzy $\sigma$-nowhere dense sets and fuzzy $\sigma$-boundary sets are fuzzy simply* closed sets in fuzzy $\partial^*$ spaces. The conditions under which a fuzzy $\partial^*$ space becomes a fuzzy weakly Baire space, and a fuzzy $P$-space becomes a fuzzy $\partial^*$ space are also obtained.
Received: January 13, 2022
Accepted: May 9, 2022
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