ブラウザの JavaScript がオフ(ブロックまたは許可しない)に設定されているため、このページは正常に機能しません。
Encyclopedia of Compactness Wiki*
[
ホーム
]
一覧
最終更新
バックアップ
ヘルプ
Top
>
m-metacompact
>
複製
?
ms
m-metacompact をテンプレートにして作成
これらのキーワードがハイライトされています:
開始行:
*Definition [#d8dac179]
m denotes an infinite cardinal.
The space X is said to be m-metacompact if and only if each open covering of X by no more than m sets admits as a refinement a [[point-finite]] open covering.
*Property [#z5e865fd]
-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 \aleph_0≦|U|≦m there is an open covering V which refines U such that each point of X belongs to less than |U| members of V.
++ 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 [#d8dac179]
m denotes an infinite cardinal.
The space X is said to be m-metacompact if and only if each open covering of X by no more than m sets admits as a refinement a [[point-finite]] open covering.
*Property [#z5e865fd]
-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 \aleph_0≦|U|≦m there is an open covering V which refines U such that each point of X belongs to less than |U| members of V.
++ 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.
ページ名: