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

 

Van Douwen's problem on 0-dimensional images
of ordered compacta


Author: S. Purisch
Journal: Proc. Amer. Math. Soc. 126 (1998), 269-271
MSC (1991): Primary 54D70, 54F05; Secondary 06A05, 54C05, 54D30, 54F50
MathSciNet review: 1452823
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Abstract: A compact 0-dimensional space has a $T_0$-separating rank 1 family of clopen sets iff it is the continuous image of a compact 0-dimensional linearly ordered space.


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Additional Information

S. Purisch
Affiliation: Department of Mathematics and Computer Science, University of Miami, Coral Gables, Florida 33124
Email: purisch@cs.miami.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04404-9
PII: S 0002-9939(98)04404-9
Keywords: 0-dimensional, continuous image, linearly ordered compactum, $T_0$-separating, rank 1, Boolean algebras, dendron
Received by editor(s): November 12, 1995
Communicated by: James West
Article copyright: © Copyright 1998 American Mathematical Society