A metric space of A. H. Stone and an example concerning minimal bases
Authors:
Harold R. Bennett and David J. Lutzer
Journal:
Proc. Amer. Math. Soc. 126 (1998), 21912196
MSC (1991):
Primary 54F05, 54D18, 54D30, 54E35
MathSciNet review:
1487358
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Abstract: In this paper we use a metric space due to A. H. Stone and one of its completions to construct a linearly ordered topological space that is \v{C}ech complete, has a closeddiscrete dense subset, is perfect, hereditarily paracompact, firstcountable, and has the property that each of its subspaces has a minimal base for its relative topology. However, is not metrizable and is not quasidevelopable. The construction of is a pointsplitting process that is familiar in ordered spaces, and an orderability theorem of Herrlich is the link between Stone's metric space and our construction.
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Additional Information
Harold R. Bennett
Affiliation:
Department of Mathematics, Texas Tech University, Lubbock, Texas 79409
David J. Lutzer
Affiliation:
Department of Mathematics, College of William and Mary, Williamsburg, Virginia 23187
DOI:
http://dx.doi.org/10.1090/S0002993998047856
PII:
S 00029939(98)047856
Keywords:
Linearly ordered space,
generalized ordered space,
\v Cech complete,
paracompact,
perfect space,
$\sigma $minimal base,
metrization theory
Received by editor(s):
April 25, 1996
Received by editor(s) in revised form:
January 1, 1997
Communicated by:
Franklin D. Tall
Article copyright:
© Copyright 1998
American Mathematical Society
