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

 

Small inductive dimension
of completions of metric spaces


Author: S. Mrówka
Journal: Proc. Amer. Math. Soc. 125 (1997), 1545-1554
MSC (1991): Primary 54F45; Secondary 54A35, 54E35, 54H05
MathSciNet review: 1423324
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Abstract | References | Similar Articles | Additional Information

Abstract: We construct a 0-dimensional metric space which under a special set-theoretic assumption, denoted in the paper as S($\aleph _{0}$), does not have a 0-dimensional completion. Shortly after the submission of the paper for publication R. Dougherty has shown the consistency of S($\aleph _{0}$). (S($\aleph _{0}$) disagrees with the continuum hypothesis.)


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Additional Information

S. Mrówka
Email: mrowka@acsu.buffalo.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-97-04132-4
PII: S 0002-9939(97)04132-4
Keywords: Inductive and covering dimension, metric spaces, completion
Received by editor(s): November 20, 1995
Communicated by: Franklin D. Tall
Article copyright: © Copyright 1997 American Mathematical Society