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AN ANSWER TO VAN MILL’S QUESTION

Part of: Spaces with richer structures Fairly general properties

Published online by Cambridge University Press:  01 December 2008

ER-GUANG YANG  and
WEI-XUE SHI
ER-GUANG YANG*
Affiliation:
Department of Mathematics, Nanjing University, Nanjing 210093, People’s Republic of China (email: [email protected])
WEI-XUE SHI
Affiliation:
Department of Mathematics, Nanjing University, Nanjing 210093, People’s Republic of China (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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van Mill et al. posed in ‘Classes defined by stars and neighborhood assignments’, Topology Appl.154 (2007), 2127–2134 the following question: Is a star-compact space metrizable if it has a Gδ-diagonal? In this paper, we give a negative answer to this question.

Keywords

star-compactmetrizabilityGδ-diagonal

MSC classification

Secondary: 54D20: Noncompact covering properties (paracompact, Lindelöf, etc.) 54E35: Metric spaces, metrizability
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 78 , Issue 3 , December 2008 , pp. 353 - 355
Copyright
Copyright © 2009 Australian Mathematical Society

Footnotes

This work is supported by NSFC, project 10571081.

References

[1]van Douwen, E. K., Reed, G. M. and Tree, I. J., ‘Star covering properties’, Topology Appl. 39 (1991), 71–103.CrossRefGoogle Scholar
[2]Gruenhage, G., ‘Generalized metric spaces’, in: Handbook of Set-Theoretic Topology (North-Holland, Amsterdam, 1984), pp. 423–501.CrossRefGoogle Scholar
[3]Matveev, M., ‘A survey on star covering properties’, Topology Atlas, Preprint No. 330, 1998.Google Scholar
[4]van Mill, J., Tkachuk, V. V. and Wilson, R. G., ‘Classes defined by stars and neighborhood assignments’, Topology Appl. 154 (2007), 2127–2134.CrossRefGoogle Scholar