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A NOTE ON MONOTONE LINDELÖFNESS OF COUNTABLE SPACES

Part of: Fairly general properties

Published online by Cambridge University Press:  09 February 2009

YAN-KUI SONG
YAN-KUI SONG*
Affiliation:
Institute of Mathematics, School of Mathematics and Computer Sciences, Nanjing Normal University, Nanjing, 210097, People’s Republic of China (email: [email protected])
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Abstract

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In this note, we give an example of a Hausdorff, countable monotone Lindelöf space which is not metrizable, which gives a negative answer to a question raised by Levy and Matveev.

Keywords

Lindelöfmonotonically Lindelöf

MSC classification

Secondary: 54D20: Noncompact covering properties (paracompact, Lindelöf, etc.)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 79 , Issue 1 , February 2009 , pp. 69 - 70
Copyright
Copyright © Australian Mathematical Society 2009

Footnotes

The author acknowledges the support from NSFC Projects 10571081 and the National Science Foundation of Jiangsu Higher Education Institutions of China (Grant No 07KJB-110055).

References

[1] Bennett, H., Lutzer, D. and Matveev, M., ‘The monotone Lindelöf property and separability in ordered spaces’, Topology Appl. 151 (2005), 180–186.CrossRefGoogle Scholar
[2] Engelking, E., General Topology, Revised and Completed Edition (Heldermann, Berlin, 1989).Google Scholar
[3] Levy, R. and Matveev, M., ‘Some more examples of monotonically Lindelöf and not monotonically Lindelöf spaces’, Topology Appl. 154 (2007), 2333–2343.CrossRefGoogle Scholar
[4] Levy, R. and Matveev, M., ‘On monotone Lindelöfness of countable spaces’, Comment. Math. Univ. Carolin. 49(1) (2008), 155–161.Google Scholar