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AN ANSWER TO VAN MILL’S QUESTION

Published online by Cambridge University Press:  01 December 2008

ER-GUANG YANG*
Affiliation:
Department of Mathematics, Nanjing University, Nanjing 210093, People’s Republic of China (email: egyang@126.com)
WEI-XUE SHI
Affiliation:
Department of Mathematics, Nanjing University, Nanjing 210093, People’s Republic of China (email: wxshi@nju.edu.cn)
*
For correspondence; e-mail: egyang@126.com
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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.

Type
Research Article
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), 71103.Google Scholar
[2]Gruenhage, G., ‘Generalized metric spaces’, in: Handbook of Set-Theoretic Topology (North-Holland, Amsterdam, 1984), pp. 423501.Google 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), 21272134.Google Scholar