A nonmetrizable compact linearly ordered topological space, every subspace of which has a minimal base
Author:
WeiXue Shi
Journal:
Proc. Amer. Math. Soc. 127 (1999), 27832791
MSC (1991):
Primary 54F05, 54G20, 54E35
Published electronically:
April 15, 1999
MathSciNet review:
1600133
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Abstract: A collection of subsets of a space is minimal if each element of contains a point which is not contained in any other element of . A base of a topological space is minimal if it can be written as a union of countably many minimal collections. We will construct a compact linearly ordered space satisfying that is not metrizable and every subspace of has a minimal base for its relative topology. This answers a problem of Bennett and Lutzer in the negative.
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Additional Information
WeiXue Shi
Affiliation:
Department of Mathematics, Changchun Teachers College, Changchun 130032, China
Address at time of publication:
Institute of Mathematics, University of Tsukuba, Tsukubashi, Ibaraki 305, Japan
Email:
shi@abel.math.tsukuba.ac.jp
DOI:
http://dx.doi.org/10.1090/S0002993999048534
PII:
S 00029939(99)048534
Keywords:
\(\sigma\)minimal base,
metrizable,
linearly ordered topological space,
special Aronszajn tree,
quasidevelopable
Received by editor(s):
October 25, 1996
Received by editor(s) in revised form:
November 15, 1997
Published electronically:
April 15, 1999
Communicated by:
Alan Dow
Article copyright:
© Copyright 1999
American Mathematical Society
