Characterizations of paracompactness and Lindelöfness by the separation property

Author:
Yukinobu Yajima

Journal:
Proc. Amer. Math. Soc. **131** (2003), 1297-1302

MSC (2000):
Primary 54B10, 54D20

Published electronically:
November 6, 2002

MathSciNet review:
1948123

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Abstract: The separation property in our title is that, for two spaces and , any two disjoint closed copies of in are separated by open sets in . It is proved that a Tychonoff space is paracompact if and only if this separation property holds for the space and every Tychonoff space which is a perfect image of (where denotes the Stone-Cech compactification of ). Moreover, we give a characterization of Lindelöfness in a similar way under the assumption of paracompactness.

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Additional Information

**Yukinobu Yajima**

Affiliation:
Department of Mathematics, Kanagawa University, Yokohama 221-8686, Japan

Email:
yajimy01@kanagawa-u.ac.jp

DOI:
http://dx.doi.org/10.1090/S0002-9939-02-06633-9

Keywords:
Paracompact,
separated by disjoint open sets,
completely separated,
Lindel\"{o}f

Received by editor(s):
May 30, 2000

Received by editor(s) in revised form:
November 12, 2001

Published electronically:
November 6, 2002

Communicated by:
Alan Dow

Article copyright:
© Copyright 2002
American Mathematical Society