ON FUZZY ESSENTIAL $P$-SPACES
Keywords:
fuzzy $G_\delta$-set, fuzzy $F_\sigma$-set, fuzzy dense set, fuzzy residual set, fuzzy door space, fuzzy almost $P$-space, fuzzy submaximal space, fuzzy perfectly disconnected space, fuzzy weakly Baire space.DOI:
https://doi.org/10.17654/0973421X22012Abstract
In this paper, the concept of a fuzzy essential $P$-space is introduced. A condition for a fuzzy door space to become a fuzzy essential $P$-space is presented. It is obtained that fuzzy essential $P$-spaces are fuzzy almost $P$-spaces, and that fuzzy weakly Baire and fuzzy essential $P$-spaces are neither fuzzy perfectly disconnected nor fuzzy hereditarily irresolvable. Fuzzy hyperconnected and fuzzy essential $P$-spaces are found to be fuzzy semi-$P$-spaces.
Received: March 14, 2022
Accepted: June 21, 2022
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