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m-quasicompact をテンプレートにして作成
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開始行:
*Definition [#hcee65d9]
-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 [#pbccfdd7]
-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 [#g998b14c]
Gulden, S. L. , Fleischman, W. M. and Weston, J. H. ,''Linearly ordered topological spaces'',Proc. Amer. Math. Soc. 24 1970 197--203.
終了行:
*Definition [#hcee65d9]
-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 [#pbccfdd7]
-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 [#g998b14c]
Gulden, S. L. , Fleischman, W. M. and Weston, J. H. ,''Linearly ordered topological spaces'',Proc. Amer. Math. Soc. 24 1970 197--203.
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