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functionally compact をテンプレートにして作成
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開始行:
*Definition [#ca825243]
-A Hausdorff topological space X is called functionally compact if whenever U is an open filter base on X such that the intersection A of the elements of U is equal to the intersection of the closures of the elements of U, then U is a base
*Property [#g1ace937]
-A functionally compact Hausdorff space is compact if and only if it is regular.
-A Hausdorff space X is functionally compact if and only if every mapping of X into any Hausdorff space is closed.
-If X is [[C-compact]] then X is functionally compact.
-Every functionally compact space is minimal Hausdorff.
-Every [[CFC>compactly functionally compact]] space is [[FFC>finitely functionally compact]] and every [[FFC>finitely functionally compact]] space is FC.
*Remark [#zbc2e048]
-It is abbreviated as FC.
-See [[finitely functionally compact]] and [[compactly functionally compact]].
*Reference [#g998b14c]
-Dickman, R. F. and Jr. Zame, A.,''Functionally compact spaces'', Pacific J. Math. 31 1969 303--311
-R.F. Dickman, Jr. and J.R. Porter, ''Between minimal Hausdorff and compact Hausdorff spaces'', Topology Proc. Vol.9 (1984), pp.243-268.
終了行:
*Definition [#ca825243]
-A Hausdorff topological space X is called functionally compact if whenever U is an open filter base on X such that the intersection A of the elements of U is equal to the intersection of the closures of the elements of U, then U is a base
*Property [#g1ace937]
-A functionally compact Hausdorff space is compact if and only if it is regular.
-A Hausdorff space X is functionally compact if and only if every mapping of X into any Hausdorff space is closed.
-If X is [[C-compact]] then X is functionally compact.
-Every functionally compact space is minimal Hausdorff.
-Every [[CFC>compactly functionally compact]] space is [[FFC>finitely functionally compact]] and every [[FFC>finitely functionally compact]] space is FC.
*Remark [#zbc2e048]
-It is abbreviated as FC.
-See [[finitely functionally compact]] and [[compactly functionally compact]].
*Reference [#g998b14c]
-Dickman, R. F. and Jr. Zame, A.,''Functionally compact spaces'', Pacific J. Math. 31 1969 303--311
-R.F. Dickman, Jr. and J.R. Porter, ''Between minimal Hausdorff and compact Hausdorff spaces'', Topology Proc. Vol.9 (1984), pp.243-268.
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