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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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