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almost realcompact をテンプレートにして作成
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*Definition [#k3ac5719]
A topological space X is said to be almost realcompact if every open ultrafilter U with the [[weak cip]] has a nonempty [[adherence>open filter adherence]].
*Property [#l7ffc21f]
-Every [[realcompact]] space is almost realcompact.
-Every normal almost realcompact space is [[realcompact]].
-Almost realcompactness of a Tychonoff space X is equivalent to the following condition: The collection of all countable open covers of X is complete.
-Alomost realcompactness is invariant under [[perfect]] mappings.
-Conversely, let X be a regular space, Y an image of a [[perfect]] mapping. If Y is almost realcompact, X is also almost realcompact.
-Every [[Lindeloef]] space is almost realcompact.
-The topological product of an arbitrary family of almost realcompact spaces is an almost realcompact space.
-Closed subspaces of a regular almost realcompact space are almost realcompact.
space.
-A Tychonoff space is almost realcompact iff every ultrafilter of [[regular closed>regular open]] sets with [[cip]] is fixed.
*Remark [#r6361f6a]
-cf. [[realcompact]], [[almost* realcompact]].
-Some authors require Tychonoffness ([Schommer, Swardson, 2001]).
*Reference [#ed7e1748]
-Zdenek Frolik, ''A generalization of realcompact spaces'', Czechoslovak Mathematical Journal, Vol.13 (1963), No. 1, 127-138.
-John J. Schommer and Mary Anne Swardson, ''Almost realcompactness'', Commentationes Mathematicae Universitatis Carolinae, Vol.2 (2001), No.2, 383-392.
終了行:
*Definition [#k3ac5719]
A topological space X is said to be almost realcompact if every open ultrafilter U with the [[weak cip]] has a nonempty [[adherence>open filter adherence]].
*Property [#l7ffc21f]
-Every [[realcompact]] space is almost realcompact.
-Every normal almost realcompact space is [[realcompact]].
-Almost realcompactness of a Tychonoff space X is equivalent to the following condition: The collection of all countable open covers of X is complete.
-Alomost realcompactness is invariant under [[perfect]] mappings.
-Conversely, let X be a regular space, Y an image of a [[perfect]] mapping. If Y is almost realcompact, X is also almost realcompact.
-Every [[Lindeloef]] space is almost realcompact.
-The topological product of an arbitrary family of almost realcompact spaces is an almost realcompact space.
-Closed subspaces of a regular almost realcompact space are almost realcompact.
space.
-A Tychonoff space is almost realcompact iff every ultrafilter of [[regular closed>regular open]] sets with [[cip]] is fixed.
*Remark [#r6361f6a]
-cf. [[realcompact]], [[almost* realcompact]].
-Some authors require Tychonoffness ([Schommer, Swardson, 2001]).
*Reference [#ed7e1748]
-Zdenek Frolik, ''A generalization of realcompact spaces'', Czechoslovak Mathematical Journal, Vol.13 (1963), No. 1, 127-138.
-John J. Schommer and Mary Anne Swardson, ''Almost realcompactness'', Commentationes Mathematicae Universitatis Carolinae, Vol.2 (2001), No.2, 383-392.
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