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

 

Consonance and topological completeness
in analytic spaces


Author: Ahmed Bouziad
Journal: Proc. Amer. Math. Soc. 127 (1999), 3733-3737
MSC (1991): Primary 54A35; Secondary 54B20, 54C60
Published electronically: May 10, 1999
MathSciNet review: 1610916
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Abstract | References | Similar Articles | Additional Information

Abstract: We give a set-valued criterion for a topological space $X$ to be consonant, i.e. the upper Kuratowski topology on the family of all closed subsets of $X$ coincides with the co-compact topology. This characterization of consonance is then used to show that the statement ``every analytic metrizable consonant space is complete'' is independent of the usual axioms of set theory. This answers a question by Nogura and Shakhmatov. It is also proved that continuous open surjections defined on a consonant space are compact covering.


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Additional Information

Ahmed Bouziad
Affiliation: Département de Mathématiques, Université de Rouen, CNRS UPRES-A 6085, 76821 Mont Saint-Aignan, France
Email: Ahmed.Bouziad@univ-rouen.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04902-3
PII: S 0002-9939(99)04902-3
Keywords: Upper Kuratowski convergence, co-compact topology, analytic spaces, consonant spaces
Received by editor(s): October 7, 1996
Received by editor(s) in revised form: February 10, 1998
Published electronically: May 10, 1999
Communicated by: Alan Dow
Article copyright: © Copyright 1999 American Mathematical Society