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


A note on paracompactness
in generalized ordered spaces

Authors: Eric K. van Douwen and David J. Lutzer
Journal: Proc. Amer. Math. Soc. 125 (1997), 1237-1245
MSC (1991): Primary 54F05, 54D20
MathSciNet review: 1396999
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Abstract: In this paper, we show that for generalized ordered spaces, paracompactness is equivalent to Property D, where a space $X$ is said to have Property D if, given any collection $\{G(x)\colon x\in X\}$ of open sets in $X$ satisfying $x\in G(x)$ for each $x$, there is a closed discrete subset $D$ of $X$ satisfying $X=\bigcup \{G(x)\colon x\in D\}$.

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Additional Information

Eric K. van Douwen
Affiliation: Department of Mathematics, Ohio University, Athens, Ohio 45701

David J. Lutzer
Affiliation: Department of Mathematics, College of William and Mary, Williamsburg, Virginia 23187

PII: S 0002-9939(97)03902-6
Keywords: Paracompactness, Property D, generalized ordered space, linearly ordered space
Received by editor(s): October 5, 1995
Communicated by: Franklin D. Tall
Article copyright: © Copyright 1997 American Mathematical Society

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