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Encyclopedia of Compactness Wiki*
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almost-compact をテンプレートにして作成
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開始行:
*Definition [#f76fe6af]
Let X be a Hausdorff space, let E be a family of open sets in X and let F denote the family of the closures of all elements in E. X is called almost-compact if F has a nonempty intersection whenever E has [[fip]].
*Property [#xfd33452]
-If X is a Hausdorff space, then almost-compactness is equivalent to the following condition: if C is a open cover of X, there is a finite subcover F of C such that the closures of the member of F cover X.
-The product of nonempty Hausdorff space is almost-compact iff each coordinate space is almost-compact (See [[almost precompact]] and [Fletcher-Naimpally]).
*Remark [#a82899cb]
-It is called [[H-closed]] in the terminology of M. Kateiov.
*Reference [#lbfc269f]
-Zdenek Frolik, ''A generalization of realcompact spaces'', Czechoslovak Mathematical Journal, Vol.13 (1963), No. 1, 127-138.
-P. Fletcher and S. Naimpally, ''On almost complete and almost precompact quasi-uniform spaces'', Czechoslovak Math. J., Vol.21 (1971), No.3, pp.383-390.
終了行:
*Definition [#f76fe6af]
Let X be a Hausdorff space, let E be a family of open sets in X and let F denote the family of the closures of all elements in E. X is called almost-compact if F has a nonempty intersection whenever E has [[fip]].
*Property [#xfd33452]
-If X is a Hausdorff space, then almost-compactness is equivalent to the following condition: if C is a open cover of X, there is a finite subcover F of C such that the closures of the member of F cover X.
-The product of nonempty Hausdorff space is almost-compact iff each coordinate space is almost-compact (See [[almost precompact]] and [Fletcher-Naimpally]).
*Remark [#a82899cb]
-It is called [[H-closed]] in the terminology of M. Kateiov.
*Reference [#lbfc269f]
-Zdenek Frolik, ''A generalization of realcompact spaces'', Czechoslovak Mathematical Journal, Vol.13 (1963), No. 1, 127-138.
-P. Fletcher and S. Naimpally, ''On almost complete and almost precompact quasi-uniform spaces'', Czechoslovak Math. J., Vol.21 (1971), No.3, pp.383-390.
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