On Hausdorffness and compactness in intuitionistic fuzzy topological spaces

Abstract

Without directly involving the roleof points, we introduce and study the notions of fuzzy$\lambda$-Hausdorff spaces and fuzzy $\mu$-compact spaces. Acharacterization of a map $f$ from a fuzzy $\lambda$-Hausdorff space$X$ to a fuzzy $\mu$-compact space $Y$, where $\lambda=f^{-1}(\mu)$,to be fuzzy $\lambda$-continuous is obtained, which puts such acharacterization for the continuity of $f$ in ordinary topologicalsetting, for fuzzy topological spaces. These notions and resultshave been formulated for intuitionistic fuzzy topological spaces also.