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

DOI:
https://doi.org/10.1090/S0002-9939-99-04902-3

Published electronically:
May 10, 1999

MathSciNet review:
1610916

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We give a set-valued criterion for a topological space to be consonant, i.e. the upper Kuratowski topology on the family of all closed subsets of 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:
https://doi.org/10.1090/S0002-9939-99-04902-3

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