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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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 $\sigma$-discrete, but which do not have a $\sigma$-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
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
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