FUZZY $\beta$-CONNECTEDNESS IN THE FUZZY TOPOLOGICAL SPACES

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.