On S-closed and extremally disconnected fuzzy topological spaces. (English) Zbl 1006.54012

Petričević, Zlata

Mat. Vesn. 50, No. 1-2, 37-45 (1998).

The concepts of \(\delta\)-convergence, \(s\)-convergence and \(\theta\)-convergence of a filter-base on a fuzzy topological space are introduced. \(S\)-closed and extremally disconnected fuzzy topological spaces are studied. Some of the results are as follows. For an fuzzy topological space \([X,\tau]\) the following propositions are equivalent: (1) \(X\) is \(S\)-closed; (2) each filter-base in \(X\) \(s\)-accumulates; (3) every maximal filter-base on \(X\) \(s\)-converges.
For an fuzzy topological space \((X,\tau)\) the following statements are equivalent: (1) \(X\) is extremally disconnected; (2) if a filter-base on \(X\) \(\delta\)-converges, then it \(s\)-converges; (3) a filter-base \(X\) \(s\)-converges iff it \(\theta\)-converges; (4) if a filter-base on \(X\) converges with respect to \(\tau\) then it \(s\)-converges.
Some properties of fuzzy compact and fuzzy regular spaces are established.

Reviewer: Dušan Adnađević (Beograd)

MSC:

54A40

Fuzzy topology

Keywords:

fuzzy filter-base; fuzzy compactness; fuzzy regularity