Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-23T16:30:49.806Z Has data issue: false hasContentIssue false
  • English
  • Français

A RESULT ON MONOTONICALLY LINDELÖF GENERALIZED ORDERED SPACES

Part of: Special properties

Published online by Cambridge University Press:  18 August 2011

AI-JUN XU  and
WEI-XUE SHI
AI-JUN XU
Affiliation:
School of Mathematical Sciences, Nanjing Normal University, Nanjing 210046, PR China (email: [email protected])
WEI-XUE SHI*
Affiliation:
Department of Mathematics, Nanjing University, Nanjing 210093, PR China (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, we show that the character of any monotonically Lindelöf generalized ordered (GO) space is not greater than ω1, which gives a negative answer to a question posed by Levy and Matveev [‘Some questions on monotone Lindelöfness’, Questions Answers Gen. Topology26 (2008), 13–27, Question 51].

Keywords

monotonically Lindelöfgeneralized ordered spaces

MSC classification

Secondary: 54F05: Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 84 , Issue 3 , December 2011 , pp. 481 - 483
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

Footnotes

This work is supported by NSFC (no:10971092), NJFU (no:163101088).

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]Engleking, R., General Topology, revised and completed edition, Sigma Series in Pure Mathematics, 6 (Hedermann, Berlin, 1989).Google Scholar
[3]Kemoto, N., ‘Normality of products of GO-spaces and cardinals’, Topology Proc. 18 (1993), 133–142.Google Scholar
[4]Levy, R. and Matveev, M., ‘Some questions on monotone Lindelöfness’, Questions Answers Gen. Topology 26 (2008), 13–27.Google Scholar
[5]Lutzer, D., ‘Ordered topological spaces’, in: Surveys in General Topology (ed. Reed, G. M.) (Academic Press, New York, 1980), pp. 247–296.CrossRefGoogle Scholar
[6]Xu, A.-J. and Shi, W.-X., ‘Notes on monotone Lindelöf property’, Czechoslovak Math. J. 59(134) (2009), 943–955.CrossRefGoogle Scholar
[7]Xu, A.-J. and Shi, W.-X., ‘Monotone Lindelöf property and linearly ordered extensions’, Bull. Aust. Math. Soc. 81 (2010), 418–424.CrossRefGoogle Scholar