Invariance of fuzzy properties. (English) Zbl 1006.54011

Lupiañez, Francisco Gallego

Mat. Vesn. 50, No. 1-2, 11-16 (1998).

Fuzzy topological spaces weakly induced by topological spaces, studied by H. W. Martin [J. Math. Anal. Appl. 78, 634-639 (1980; Zbl 0463.54007)] are considered. Let \((X,T)\) and \((Y,S)\) be two weakly fuzzy topological spaces induced by topological spaces \((X,[T])\), \((Y,[S])\) respectively. Let \(\omega:Top\to CFT\) be a functor that associates to any topological space \((X,T)\) the fuzzy space \((X,\omega T)\) (defined by R. Lowen [ibid. 64, 446-454 (1978; Zbl 0381.54004)]). Various types of maps \(\omega(f):(X,T)\to(Y,S)\) and of corresponding maps \(f:(X,[T])\to(Y,[S])\) are studied (continuous, open, closed perfect and other).
The invariance and the invariance under these maps of different properties of fuzzy topological spaces are investigated.

Reviewer: Dušan Adnađević (Beograd)

MSC:

54A40

Fuzzy topology

Keywords:

fuzzy topological map; fuzzy perfect map

Citations:

Zbl 0463.54007; Zbl 0381.54004