Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 $X=\bigcup \{G(x)\colon x\in D\}$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 54F05, 54D20

Retrieve articles in all journals with MSC (1991): 54F05, 54D20

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

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