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MONOTONE LINDELÖF PROPERTY AND LINEARLY ORDERED EXTENSIONS

Part of: Fairly general properties Special properties

Published online by Cambridge University Press:  05 March 2010

AI-JUN XU  and
WEI-XUE SHI
AI-JUN XU*
Affiliation:
Department of Applied Mathematics, Nanjing Forest University, Nanjing 210037, PR China (email: ajxu@njfu.edu.cn)
WEI-XUE SHI
Affiliation:
Department of Mathematics, Nanjing University, Nanjing 210093, PR China (email: wxshi@nju.edu.cn)
*
✉For correspondence; e-mail: ajxu@njfu.edu.cn
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Abstract

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In this paper, we explore the monotone Lindelöf property of two kinds of linearly ordered extensions of monotonically Lindelöf generalized ordered spaces. In addition, we construct nonseparable monotonically Lindelöf spaces using the Bernstein set, which generalizes Corollary 4 of Levy and Matveev [‘Some more examples of monotonically Lindelöf and not monotonically Lindelöf spaces’, Topology Appl.154 (2007), 2333–2343].

Keywords

monotone Lindelöf propertylinearly ordered extensionlexicographic product

MSC classification

Secondary: 54F05: Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces 54D65: Separability
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 81 , Issue 3 , June 2010 , pp. 418 - 424
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

Footnotes

This work is supported by the NSFC, project 10971092.

References

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