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Consonance and topological completeness in analytic spaces
Author(s):
Ahmed
Bouziad
Journal:
Proc. Amer. Math. Soc.
127
(1999),
3733-3737.
MSC (1991):
Primary 54A35;
Secondary 54B20, 54C60
Posted:
May 10, 1999
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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:
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
Posted:
May 10, 1999
Communicated by:
Alan Dow
Copyright of article:
Copyright
1999,
American Mathematical Society
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