Relative Collectionwise Normality

Eliser Grabner, Gary Grabner, Kazumi Miyazaki, Jamal Tartir


In this paper we study properties of relative collectionwise normality type based on relative properties of normality type introduced by Arhangel’skii and Genedi.

Theorem Suppose Y is strongly regular in the space X. If Y is paracompact in X then Y is collectionwise normal in X.

Example A T2 space X having a subspace which is 1− paracompact in X but not collectionwise normal in X.

Theorem Suppose that Y is s- regular in the space X. If Y is metacompact in X and strongly collectionwise normal in X then Y is paracompact in X.


Paracompact; Collectionwise normal; Relative topological properties

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