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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Base-cover paracompactness


Author: Strashimir G. Popvassilev
Journal: Proc. Amer. Math. Soc. 132 (2004), 3121-3130
MSC (2000): Primary 54D20, 54D70, 54F05; Secondary 54D55, 54B05, 54B10, 06A05, 03E15, 03E35
Published electronically: May 12, 2004
MathSciNet review: 2063135
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Abstract: Call a topological space $X$ base-cover paracompact if $X$ has an open base $\mathcal{B}$ such that every cover $\mathcal{C}\subset\mathcal{B}$ of $X$ contains a locally finite subcover. A subspace of the Sorgenfrey line is base-cover paracompact if and only if it is $F_\sigma$. The countable sequential fan is not base-cover paracompact. A paracompact space is locally compact if and only if its product with every compact space is base-cover paracompact.


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Additional Information

Strashimir G. Popvassilev
Affiliation: Department of Mathematics, University of Louisiana at Lafayette, 217 Maxim D. Doucet Hall, P.O. Box 41010, Lafayette, Louisiana 70504-1010
Email: popvast@auburn.edu, pgs2889@louisiana.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07457-X
PII: S 0002-9939(04)07457-X
Keywords: Base-cover paracompact, GO-space, sequential fan, $D$-space
Received by editor(s): November 20, 2002
Received by editor(s) in revised form: June 28, 2003
Published electronically: May 12, 2004
Additional Notes: The author was supported in part by National Science Fund of Bulgaria Grant MM–1105/2001
Communicated by: Alan Dow
Article copyright: © Copyright 2004 American Mathematical Society