In this paper, a new class of fuzzy topological spaces, namely, fuzzy spaces, is introduced and studied. It is obtained that fuzzy G_δ-sets are fuzzy somewhere dense sets but not fuzzy simply open sets, and fuzzy F_σ-sets are fuzzy cs dense sets but not fuzzy dense sets. Fuzzy σ-nowhere dense sets and fuzzy σ-boundary sets are fuzzy simply* closed sets in fuzzy spaces. The conditions under which a fuzzy  space becomes a fuzzy weakly Baire space, and a fuzzy P-space becomes a fuzzy  space are also obtained.

fuzzy G_δ-set, fuzzy F_σ-set, fuzzy nowhere dense set, fuzzy residual set, fuzzy simply* open set, fuzzy hyperconnected space, fuzzy P-space, fuzzy weakly Baire space.

Received: January 13, 2022; Accepted: May 9, 2022; Published: September 10, 2022

How to cite this article: G. Thangaraj and J. Premkumar, On fuzzy  spaces, Advances in Fuzzy Sets and Systems 27(2) (2022), 169-188. http://dx.doi.org/10.17654/0973421X22009

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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