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THE D-PROPERTY AND THE SORGENFREY LINE

Part of: Maps and general types of spaces defined by maps Peculiar spaces Fairly general properties

Published online by Cambridge University Press:  08 June 2009

YIN-ZHU GAO  and
WEI-XUE SHI
YIN-ZHU GAO*
Affiliation:
Department of Mathematics, Nanjing University, Nanjing 210093, PR China (email: yzgao@jsmail.com.cn)
WEI-XUE SHI
Affiliation:
Department of Mathematics, Nanjing University, Nanjing 210093, PR China (email: wxshi@nju.edu.cn)
*
✉For correspondence; e-mail: yzgao@jsmail.com.cn
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Abstract

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We show that for the Sorgenfrey line S, the minimal dense linearly ordered extension of S is a D-space, but not a monotone D-space; the minimal closed linearly ordered extension of S is not a monotone D-space; the monotone D-property is inversely preserved by finite-to-one closed mappings, but cannot be inversely preserved by perfect mappings.

Keywords

Sorgenfrey linereal linelinearly ordered topological spacemonotone D-space

MSC classification

Secondary: 54D20: Noncompact covering properties (paracompact, Lindelöf, etc.) 54G15: Pathological spaces 54C25: Embedding
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 80 , Issue 2 , October 2009 , pp. 233 - 236
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2009

Footnotes

The project is supported by NSFC (No.10571081).

References

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