On spaces with the property (wa)

Authors

  • Yan-Kui Song Nanjing normal university

DOI:

https://doi.org/10.4995/agt.2006.1938

Keywords:

Property (a), Property (wa)

Abstract

A space X has the property (wa) (or is a space with the property (wa)) if for every open cover U of X and every dense subspace D of X, there exists a discrete subspace F C D such that St(F, U) = X. In this paper, we give an example of a Tychonoff space without the property (wa), and also study topological properties of spaces with the property (wa) by using the example.

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Author Biography

Yan-Kui Song, Nanjing normal university

Department of Mathematics

References

R. Engelking, General Topology, Revised and completed edition Heldermann, Berlin (1989).

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M. V. Matveev, A survey on star-covering properties, Topological Atlas, preprint No. 330 (1998).

W. Just, M. V. Matveev and P. J. Szeptycki, Some results on property (a), Topology Appl. 100 (2000), 67–83. http://dx.doi.org/10.1016/S0166-8641(98)00134-5

Y. Song, Absolutely countably compact spaces and related spaces, General and Geometric Topology (in Japan) Kyoto. 1074 (1999), 55–60.

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Z. Yang, A method constructing Hausdorff spaces without property (wa), Quest. Answers Gen. Topology 18 (2000), 113–116.

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How to Cite

[1]
Y.-K. Song, “On spaces with the property (wa)”, Appl. Gen. Topol., vol. 7, no. 1, pp. 131–138, Apr. 2006.

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