On the goodness of some types of fuzzy paracompactness
The authors introduce the definitions of paracompactness, almost paracompactness, nearly paracompactness, semi-paracompactness, para-\(S\)- closedness, weakly paracompactness and \(RS\)-paracompactness in fuzzy setting along the lines of Lowen's fuzzy compactness. To introduce the above concepts the authors adopt the concept of locally finite families of fuzzy sets and the concept of refinement introduced by Malghan and Benchalli. For a topological space \((X,\tau)\) and its generated fuzzy topological space \(\omega (t)\) the authors prove that ``\((X,\omega(t))\) is paracompact if and only if \((X,\tau)\) is paracompact. Thus fuzzy paracompactness is a good extension of paracompactness''. The authors produce analogous forms of good extensions of the other concepts introduced in this work. They conjecture that fuzzy \(RS\)-paracompactness is also good, they could'nt complete a proof of this.
scientific article; zbMATH DE number 487525