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Aull-paracompactness and strong star-normality of subspaces in topological spaces. (English) Zbl 1099.54023
The main result is the following theorem: Let \(X\) be a \(T_1\)-space and \(Y\) be a subspace of \(X\). Then the following assertions are equivalent: (1) \(Y\) is strongly star-normal in \(X\); (2) \(Y\) is strictly Aull-paracompact in \(X\) and \(Y\) is Hausdorff in \(X\); (3) \(Y\) is Aull-paracompact in \(X\) and \(Y\) is Hausdorff in \(X\); (4) \(X_Y\) (the space made from \(X\) by making all points of \(X\setminus Y\) isolated) is Hausdorff and paracompact.
MSC:
54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)
54B05 Subspaces in general topology
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