On L-smooth compactness (Q2731735)

In the paper [\textit{H. Aygün}, \textit{M. W. Warner}, and \textit{S. R. T. Kudri}, ibid. 5, No. 2, 321-338 (1997; Zbl 0880.54008)] the authors introduced a functor \(W\) from the category TOP of topological spaces into the category L-FTOP of ``smooth'' L-fuzzy topological spaces, see [\textit{A. Šostak}, Russ. Math. Surv. 44, No. 6, 125-186 (1989); translation from Usp. Mat. Nauk 44, No. 6(270), 99-147 (1989; Zbl 0716.54004)] and they used this functor for the study of compactness-type properties in L-FTOP, defined in the same work.NEWLINENEWLINENEWLINEThe aim of the present paper is to introduce properties of almost compactness, near compactness and light compactness in L-FTOP and to apply functor \(W\) for the study of these properties. Note, that unfortunately in some cases, in the paper corresponding references are missing. This concerns in particular, Theorems 5.1, 7.3, and 7.6 and Corollary 7.1, which are either identical or similar to analogous statements from the above mentioned paper by H. Aygün, M. W. Warner and S. R. T. Kudri.