A new form of fuzzy \(\alpha \)-compactness. (English) Zbl 1108.54009

Shi, Fu-Gui

Math. Bohem. 131, No. 1, 15-28 (2006).

Summary: A new form of \(\alpha \)-compactness is introduced in \(L\)-topological spaces by means of \(\alpha \)-open \(L\)-sets and their inequality where \(L\) is a complete de Morgan algebra. This notion doesn’t rely on the structure of the basis lattice \(L\). It can also be characterized by means of \(\alpha \)-closed \(L\)-sets and their inequality. When \(L\) is a completely distributive de Morgan algebra, many characterizations are presented and the relation between our new notion and other types of compactness are discussed. Countable \(\alpha \)-compactness and the \(\alpha \)-Lindelöf property are also investigated.

MSC:

54A40	Fuzzy topology
54D35	Extensions of spaces (compactifications, supercompactifications, completions, etc.)

Keywords:

\(L\)-topology; compactness