Relative Collectionwise Normality

Eliser Grabner, Gary Grabner, Kazumi Miyazaki, Jamal Tartir

Abstract

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.


Keywords

Paracompact; Collectionwise normal; Relative topological properties

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References

A. Arhangel’skii, “From classic topological invariants to relative topological properties”, Scientiae Math. Japonicae 55 No 1 (2002), 153-201.

A. Arhangel’skii and H Genedi, “Beginnings of the theory of relative topological properties”, Gen. Top. Spaces and Mappings (MGU, Moscow, 1989), 3-48 (in Russian).

A. Arhangel’skii and H Genedi, “Position of subspaces in spaces: relative versions of compactness, Lindel¨of properties, and separation axioms”, Vestnik Moskovskogo Universiteta, Mathematika 44 No. 6 (1989), 67-69.

A. Arhangel’skii and I. Gordienko, “Relative symmetrizability and metrizability”, Comment. Math. Univ. Carol. 37 No 4 (1996), 757-774.

R. Engelking, “General Topology” (PWN, Warsaw, 1977).

I. Gordienko, “On Relative Properties of Paracompactness and Normality Type”, Moscow Univ. Nath. Bul. 46 No. 1 (1991), 31-32.

E. Grabner, G. Grabner and K. Miyazaki, “ Properties of relative metacompactness and paracompactness type”, Topology Proc. 25 (2000), 145-178.

K. Miyazaki, “On relative paracompactness and characterizations of spaces by relative topological properties”, Math. Japonica 50 (1999), 17-23.

J.C. Smith and L.L. Krajewski, “Expandability and collectionwise normality”, Trans. Amer. Math. Soc. 160 (1971), 437-451.

Y. Yasui, “Results on relatively countably paracompact spaces”, Q and A in Gen. Top. 17 (1999), 165-174.

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Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt