Perfectly normal non-metrizable non-Archimedean spaces are generalized Souslin lines

Authors:
Yuan-Qing Qiao and Franklin D. Tall

Journal:
Proc. Amer. Math. Soc. **131** (2003), 3929-3936

MSC (2000):
Primary 54F05, 54A35; Secondary 03E05, 03E35

Published electronically:
July 16, 2003

MathSciNet review:
1999943

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Abstract: In this paper we prove the equivalence between the existence of perfectly normal, non-metrizable, non-archimedean spaces and the existence of ``generalized Souslin lines", *i.e.,* linearly ordered spaces in which every collection of disjoint open intervals is -discrete, but which do not have a -discrete dense set. The key ingredient is the observation that every first countable linearly ordered space has a dense non-archimedean subspace.

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Additional Information

**Yuan-Qing Qiao**

Affiliation:
Department of Mathematics, University of Toronto, Toronto, Canada M5S 3G3

**Franklin D. Tall**

Affiliation:
Department of Mathematics, University of Toronto, Toronto, Canada M5S 3G3

DOI:
http://dx.doi.org/10.1090/S0002-9939-03-06966-1

Keywords:
Non-archimedean,
perfect,
metrizable,
tree base,
generalized Souslin line,
generalized Lusin line,
$\sigma$-discrete chain condition

Received by editor(s):
December 10, 1992

Received by editor(s) in revised form:
July 5, 2002

Published electronically:
July 16, 2003

Additional Notes:
The authors acknowledge support from grant A-7354 of the Natural Sciences and Engineering Research Council of Canada

Communicated by:
Andreas Blass

Article copyright:
© Copyright 2003
American Mathematical Society