Countable compactness and the Lindelöf property of \(L\)-fuzzy sets. (English) Zbl 1202.54007

Shi, Fu-Ghi

Iran. J. Fuzzy Syst. 1, No. 1, 79-88 (2004).

Summary: Countable compactness and the Lindelöf property are defined for \(L\)-fuzzy sets, where \(L\) is a complete de Morgan algebra. They don’t rely on the structure of the basis lattice \(L\) and no distributivity is required in \(L\). A fuzzy compact \(L\)-set is countably compact and has the Lindelöf property. An \(L\)-set having the Lindelöf property is countably compact if and only if it is fuzzy compact. Many characterizations of countable compactness and the Lindelöf property are presented by means of open \(L\)-sets and closed \(L\)-sets when \(L\) is a completely distributive de Morgan algebra.

MSC:

54A40

Fuzzy topology