Normality and Paracompactness in Fuzzy Topological Spaces

Abstract

The importance of paracompactness (and the concepts related to it) in the field of Topology is well known.

In this paper we obtain two characterizations of normal fuzzy topological spaces using Luo’s and Abd El-Monsef and others’ paracompact fuzzy topological spaces. Thus, it shows that normality of fuzzy topological spaces can be considered as a paracompact-type property with several kinds of paracompact fuzzy topological spaces. Indeed, we prove that for a fuzzy Hausdorff fuzzy topological space (in any of Wuyts and Lowen’s definitions that are good extensions of Hausdorffness) there is a characterization using Luo’s paracompact fuzzy topological spaces, and also another result with a characterization using definition due to Abd El-Monsef, Zeyada, El-Deeb, and Hanafy. This supposes a stimulus for further investigations, tending to obtain characterizations of other fuzzy separation properties (for example fuzzy complete regularity) as fuzzy covering properties.