Research Article
On Fuzzy Baire-Separated Spaces and Related Concepts
Ganesan Thangaraj*,
Natarajan Raji
Issue:
Volume 13, Issue 1, February 2024
Pages:
1-8
Received:
Jan. 22, 2024
Accepted:
Feb. 27, 2024
Published:
Mar. 20, 2024
DOI:
10.11648/j.pamj.20241301.11
Downloads:
Views:
Abstract: In this paper, a new class of fuzzy topological spaces, namely fuzzy Baire-separated spaces is introduced in terms of fuzzy Baire sets. Several characterizations of fuzzy Baire-separated spaces are established. It is shown that fuzzy Baire sets lie between disjoint fuzzy P-sets and fuzzy Fσ- sets in a fuzzy Baire-separated space. Conditions under which fuzzy topological spaces become fuzzy Baire-separated spaces are established. Fuzzy nowhere dense sets are fuzzy closed sets in fuzzy nodec spaces and subsequently a question will arise. Which fuzzy topological spaces [other than fuzzy hyperconnected spaces, fuzzy globally disconnected spaces] have fuzzy closed sets with fuzzy nowhere denseness? For this, fuzzy topological spaces having fuzzy closed sets with fuzzy nowhere denseness are identified in this paper. It is verified that fuzzy ultraconnected spaces are non fuzzy Baire -separated spaces. The means, by which fuzzy weakly Baire space become fuzzy Baire -separated spaces and in turn fuzzy Baire - separated spaces become fuzzy seminormal spaces, are obtained. There are scope in this paper for exploring the inter-relations between fuzzy Baire spaces and Baire -separated spaces.
Abstract: In this paper, a new class of fuzzy topological spaces, namely fuzzy Baire-separated spaces is introduced in terms of fuzzy Baire sets. Several characterizations of fuzzy Baire-separated spaces are established. It is shown that fuzzy Baire sets lie between disjoint fuzzy P-sets and fuzzy Fσ- sets in a fuzzy Baire-separated space. Conditions under w...
Show More