On some modifications of fuzzy topology. (English) Zbl 0705.54007

Shostak, A. P.

Mat. Vesn. 41, No. 1, 51-64 (1989).

Let FT be the category of (generalized) fuzzy topological spaces studied in an earlier paper of the author [Rend. Circ. Mat. Palermo, II. Ser. Suppl. 11, 89-103 (1985; Zbl 0638.54007)]. In General topology and its relations to modern analysis and algebra VI, Proc. 6th Symp., Prague/Czech. 1986, Res. Expo. Math. 16, 519-532 (1988; Zbl 0638.54008) and Latv. Mat. Ezheg. 33, 207-212, 213-220 (1989; see the two preceding reviews), the author introduced the so-called spectra of compactness, connectedness, countable compactness and Lindelöfness of a fuzzy set in a space of FT. He defines four functors from FT to FT and relates these spectra of a fuzzy set in a given space of FT to the corresponding spectra of the same fuzzy set in the images of the given space under those four functors.

Reviewer: T.Kubiak

MSC:

54A40	Fuzzy topology
54D20	Noncompact covering properties (paracompact, Lindelöf, etc.)
54D30	Compactness

Keywords:

spectra of compactness, connectedness, countable compactness and Lindelöfness; spectra of a fuzzy set

Citations:

Zbl 0638.54007; Zbl 0638.54008