Definition
- A topological space X is m-quasicompact if and only if each open cover U of X by cozero sets, with the cardinality of U at most m, has a finite subcover. (m is infinite cardinal.)
Property
- Completely regular Hausdorff space is m-quasicompact if and only if it is m-pseudocompact.
- Let X be a linearly ordered space, and let m be an infinite carinal. The following are then equivalent:
- X is m-bounded
- X is m-compact
- X is m-pseudocompact
- X is m-quasicompact
- For each gap u of X, |ω_{α(u)}|>m and |ω_{β(u)}|>m .
Reference
Gulden, S. L. , Fleischman, W. M. and Weston, J. H. ,Linearly ordered topological spaces,Proc. Amer. Math. Soc. 24 1970 197--203.