Abstract

This paper investigates the concept of fuzzy $\beta$-connectedness in fuzzy topological spaces by introducing fuzzy $\beta$-separated sets and related constructs. We define fuzzy $\beta$-disconnected spaces and fuzzy $\beta$-connected spaces using fuzzy $\beta$-open sets. Several theorems are established to characterize the behavior and properties of these notions. We also examine the preservation of fuzzy $\beta$-connectedness under M-fuzzy $\beta$-continuous and fuzzy $\beta$-open mappings. Illustrative examples are provided to demonstrate the theoretical developments and their implications in the broader context of fuzzy topological spaces. 

Keywords and Phrases

Fuzzy topological spaces, fuzzy $\beta$-open sets, fuzzy $\beta$-separated sets, fuzzy $\beta$-disconnected sets, fuzzy $\beta$-disconnected spaces.

A.M.S. subject classification

54A40, 54D05, 03E72, 06D72.

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