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m-paracompact をテンプレートにして作成
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開始行:
*Definition [#td8598b3]
m denotes an infinite cardinal.
The space X is said to be m-paracompact if and only if each open covering of X by no moer than m sets admits as a refinement a [[locally finite]] open covering.
*Property [#j9253dd1]
-Let X be a linearly ordered space, and let m be an infinite cardinal. The following are then equivalent:
++ X is m-fully normal.
++ To each open covering U of X there corresponds a [[star-finite]] open covering V which is an m-quasi-refinement of U.
++ X is almost m-fully normal.
++ X is [[strongly m-paracompact]].
++ X is m-paracompact.
++ X is [[m-metacompact]].
++ Each open covering U of X with |U|≦m admits as a refinement an open covering V which is point countable (that is, no point of X belongs to more than contably many members of V).
++ For each open covering U of X with &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$%5caleph_0%20%5cle%20%7cU%7c%5cle%20m$%7d%25.png); there is an open covering V which refines U such that each point of X belongs to less th
++ Each gap u of X satisfying |ω_α(u)|≦m (respectively,|ω_β(u)|≦m) is a Q-gap from the left (respectively, right).
*Remark [#zbc2e048]
*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 [#td8598b3]
m denotes an infinite cardinal.
The space X is said to be m-paracompact if and only if each open covering of X by no moer than m sets admits as a refinement a [[locally finite]] open covering.
*Property [#j9253dd1]
-Let X be a linearly ordered space, and let m be an infinite cardinal. The following are then equivalent:
++ X is m-fully normal.
++ To each open covering U of X there corresponds a [[star-finite]] open covering V which is an m-quasi-refinement of U.
++ X is almost m-fully normal.
++ X is [[strongly m-paracompact]].
++ X is m-paracompact.
++ X is [[m-metacompact]].
++ Each open covering U of X with |U|≦m admits as a refinement an open covering V which is point countable (that is, no point of X belongs to more than contably many members of V).
++ For each open covering U of X with &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$%5caleph_0%20%5cle%20%7cU%7c%5cle%20m$%7d%25.png); there is an open covering V which refines U such that each point of X belongs to less th
++ Each gap u of X satisfying |ω_α(u)|≦m (respectively,|ω_β(u)|≦m) is a Q-gap from the left (respectively, right).
*Remark [#zbc2e048]
*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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