GO-spaces with -closed discrete dense subsets

Authors:
Harold R. Bennett, Robert W. Heath and David J. Lutzer

Journal:
Proc. Amer. Math. Soc. **129** (2001), 931-939

MSC (1991):
Primary 54F05, 54E35; Secondary 54D15

DOI:
https://doi.org/10.1090/S0002-9939-00-05582-9

Published electronically:
October 16, 2000

MathSciNet review:
1707135

Full-text PDF

Abstract | References | Similar Articles | Additional Information

In this paper we study the question ``When does a perfect generalized ordered space have a -closed-discrete dense subset?'' and we characterize such spaces in terms of their subspace structure, -mappings to metric spaces, and special open covers. We also give a metrization theorem for generalized ordered spaces that have a -closed-discrete dense set and a weak monotone ortho-base. That metrization theorem cannot be proved in ZFC for perfect GO-spaces because if there is a Souslin line, then there is a non-metrizable, perfect, linearly ordered topological space that has a weak monotone ortho-base.

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Additional Information

**Harold R. Bennett**

Affiliation:
Department of Mathematics, Texas Tech University, Lubbock, Texas 79409

**Robert W. Heath**

Affiliation:
Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15213

**David J. Lutzer**

Affiliation:
Department of Mathematics, College of William and Mary, Williamsburg, Virginia 23187

Email:
lutzer@math.wm.edu

DOI:
https://doi.org/10.1090/S0002-9939-00-05582-9

Keywords:
Generalized ordered space,
linearly ordered space,
perfect,
$\sigma$-discrete dense subset,
$G_\delta$-diagonal,
metrization,
weak monotone ortho-base,
Souslin line

Received by editor(s):
September 9, 1998

Received by editor(s) in revised form:
June 6, 1999

Published electronically:
October 16, 2000

Dedicated:
Dedicated to the memory of F. Burton Jones

Communicated by:
Alan Dow

Article copyright:
© Copyright 2000
American Mathematical Society