Relative Collectionwise Normality

Eliser Grabner; Gary Grabner; Kazumi Miyazaki; Jamal Tartir

doi:10.4995/agt.2004.1970

Authors

Eliser Grabner Slippery Rock University
Gary Grabner Slippery Rock University
Kazumi Miyazaki Osaka Elector-Communication University
Jamal Tartir Youngstown State University

DOI:

https://doi.org/10.4995/agt.2004.1970

Keywords:

Paracompact, Collectionwise normal, Relative topological properties

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 1âˆ’ 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.

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Author Biographies

Eliser Grabner, Slippery Rock University

Dept. Math.

Gary Grabner, Slippery Rock University

Dept. Math.

Kazumi Miyazaki, Osaka Elector-Communication University

Dept. Math.

Jamal Tartir, Youngstown State University

Dept. Math. and Stat.

References

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