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weakly Hausdorff をテンプレートにして作成
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開始行:
*Definition [#ifd20f4c]
-A topological space (X,τ) is called weakly Hausdorff if each singleton is [[δ-closed]].
*Property [#a3d0c2fb]
-A topological space (X,τ) is weakly Hausdorff if and only if every subset is [[η-open]].
-For a topological space (X,τ) the following conditions are equivalent;
++X is weakly Hausdorff.
++X is [[almost weakly Hausdorff]] and [[mildly Hausdorff]].
++X is [[almost weakly Hausdorff]] and [[weakly mildly Hausdorff]].
-Every weakly Hausdorff [[S-closed]] space is [[extremally disconnected]] and [[Urysohn]].
*Reference [#ud13f2f0]
-Dontchev, J.; Popvassilev, S.; Stavrova, D., ''On the η-expansion topology for the co-semi-regularization and mildly Hausdorff spaces.'', (English summary), Acta Math. Hungar. 80 (1998), no. 1-2, 9-19.
終了行:
*Definition [#ifd20f4c]
-A topological space (X,τ) is called weakly Hausdorff if each singleton is [[δ-closed]].
*Property [#a3d0c2fb]
-A topological space (X,τ) is weakly Hausdorff if and only if every subset is [[η-open]].
-For a topological space (X,τ) the following conditions are equivalent;
++X is weakly Hausdorff.
++X is [[almost weakly Hausdorff]] and [[mildly Hausdorff]].
++X is [[almost weakly Hausdorff]] and [[weakly mildly Hausdorff]].
-Every weakly Hausdorff [[S-closed]] space is [[extremally disconnected]] and [[Urysohn]].
*Reference [#ud13f2f0]
-Dontchev, J.; Popvassilev, S.; Stavrova, D., ''On the η-expansion topology for the co-semi-regularization and mildly Hausdorff spaces.'', (English summary), Acta Math. Hungar. 80 (1998), no. 1-2, 9-19.
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