Aull-paracompactness and strong star-normality of subspaces in topological spaces. (English) Zbl 1099.54023

Yamazaki, Kaori

Commentat. Math. Univ. Carol. 45, No. 4, 743-747 (2004).

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.

Reviewer: Ondřej Kalenda (Praha)

MSC:

54D20	Noncompact covering properties (paracompact, Lindelöf, etc.)
54B05	Subspaces in general topology

Keywords:

Aull-paracompactness of \(Y\) in \(X\); strong star-normality of \(Y\) in \(X\); fully normal space; paracompact space