Perfectly normal non-metrizable non-Archimedean spaces are generalized Souslin lines
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- by Yuan-Qing Qiao and Franklin D. Tall PDF
- Proc. Amer. Math. Soc. 131 (2003), 3929-3936 Request permission
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.References
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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
- MR Author ID: 170400
- 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
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 3929-3936
- MSC (2000): Primary 54F05, 54A35; Secondary 03E05, 03E35
- DOI: https://doi.org/10.1090/S0002-9939-03-06966-1
- MathSciNet review: 1999943