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arXiv · 2509.11556

Separation Axioms in Fuzzy Closure Spaces

Albin James·T. P. Johnson
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Abstract

Fuzzy closure spaces are an extension of classical closure spaces in topology, where the concept of closure is defined in terms of fuzzy sets. This article introduces interior operators and neighborhood systems in fuzzy closure spaces. Using that, we have redefined \v{C}F-continuity. Separation axioms such as $\v{C}FT_0$, $\v{C}FT_1$, $\v{C}FT_2$, \v{C}F-Urysohn, \v{C}F-regular, and \v{C}F-normal in fuzzy closure spaces are introduced using these neighborhood systems. Additive, productive, hereditary, and other properties of these axioms have been observed. Relationships between these axioms are also investigated.

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Albin James, T. P. Johnson. 2025-09-15. Separation Axioms in Fuzzy Closure Spaces. https://arxiv.org/abs/2509.11556

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