Small inductive dimension of completions of metric spaces

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-dimen\-sio\-nal completion. Shortly after the submission of the paper for publication R. Dougherty has shown the consistency of S(\aleph _{0}). (S(\alep...

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Bibliographic Details
Published in:	Proceedings of the American Mathematical Society Vol. 125; no. 5; pp. 1545 - 1554
Main Author:	S. Mrówka
Format:	Journal Article
Language:	English
Published:	American Mathematical Society 01-05-1997
Subjects:	Cantor set Cardinality Continuum hypothesis Dyadics General topology Inductive dimensions Mathematical set theory Parallel lines Topology Uniformity completion Inductive and covering dimension metric spaces
Online Access:	Get full text
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Summary:	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-dimen\-sio\-nal 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.)
ISSN:	0002-9939 1088-6826
DOI:	10.1090/S0002-9939-97-04132-4