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A NOTE ON CONTINUOUSLY URYSOHN SPACES

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

Published online by Cambridge University Press:  02 July 2009

JIAN-SHENG CHEN  and
WEI-XUE SHI
JIAN-SHENG CHEN*
Affiliation:
Department of Mathematics, Nanjing University, Nanjing 210093, People’s Republic of China (email: [email protected])
WEI-XUE SHI
Affiliation:
Department of Mathematics, Nanjing University, Nanjing 210093, People’s Republic of China (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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In this paper, we generalize a result of Bennett and Lutzer and give a condition under which a continuously Urysohn space must have a one-parameter continuous separating family.

Keywords

continuously Urysohn spacescontinuous separating familyone-parameter continuous separating family

MSC classification

Secondary: 54F65: Topological characterizations of particular spaces 54C30: Real-valued functions 54D65: Separability
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 80 , Issue 3 , December 2009 , pp. 472 - 475
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2009

Footnotes

This work was supported by the NSF of China as project no. 10571081

References

[1]Arhangel’skii, A. V., ‘On a class of spaces containing all metric and all locally bicompact spaces’, Dokl. Akad. Nauk SSSR 151 (1963), 751–754.Google Scholar
[2]Bennett, H. R. and Lutzer, D. J., ‘Continuous separating families in ordered spaces and strong base conditions’, Topology Appl. 119 (2002), 305–314.CrossRefGoogle Scholar
[3]Halbeisen, L. and Hungerbühler, N., ‘On continuously Urysohn and strongly separating spaces’, Topology Appl. 118 (2002), 329–335.CrossRefGoogle Scholar
[4]Shi, W.-X. and Gao, Y.-Z., ‘Sorgenfrey line and continuous separating families’, Topology Appl. 142 (2004), 89–94.CrossRefGoogle Scholar
[5]Stepanova, E. N., ‘Continuation of continuous functions and the metrizability of paracompact p-space’, Math. Notes 53(3–4) (1993), 308–314; translated from Mat. Zametki 53(3) (1993), 92–101.CrossRefGoogle Scholar
[6]Stepanova, E. N., ‘On the metrizability of paracompact p-space’, Moscow Univ. Math. Bull. 49(6) (1994), 41–43; translated from Vestnik. Moskov. Univ. Ser. I Mat. Mekh. OVYR(6) (1994), 69–71.Google Scholar