Consonance and topological completeness in analytic spaces
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- by Ahmed Bouziad
- Proc. Amer. Math. Soc. 127 (1999), 3733-3737
- DOI: https://doi.org/10.1090/S0002-9939-99-04902-3
- Published electronically: May 10, 1999
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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.References
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Bibliographic 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
- 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
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 3733-3737
- MSC (1991): Primary 54A35; Secondary 54B20, 54C60
- DOI: https://doi.org/10.1090/S0002-9939-99-04902-3
- MathSciNet review: 1610916