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Perfectly normal non-metrizable non-Archimedean spaces are generalized Souslin lines
Author(s):
Yuan-Qing
Qiao;
Franklin
D.
Tall
Journal:
Proc. Amer. Math. Soc.
131
(2003),
3929-3936.
MSC (2000):
Primary 54F05, 54A35;
Secondary 03E05, 03E35
Posted:
July 16, 2003
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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:
10.1090/S0002-9939-03-06966-1
PII:
S 0002-9939(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
Posted:
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
Copyright of article:
Copyright
2003,
American Mathematical Society
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