k-spaces and Borel filters on the set of integers
Author:
Jean Calbrix
Journal:
Trans. Amer. Math. Soc. 348 (1996), 2085-2090
MSC (1991):
Primary :, 03E15, 04A15, 54-05; Secondary 54C35
DOI:
https://doi.org/10.1090/S0002-9947-96-01635-2
MathSciNet review:
1355296
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Abstract | References | Similar Articles | Additional Information
Abstract: We say that a countable, Hausdorff, topological space with one and only one accumulation point is a point-space. For such a space, we give several properties which are equivalent to the property of being a k-space. We study some free filters on the set of integers and we determine if the associated point-spaces are k-spaces or not. We show that the filters of Lutzer-van Mill-Pol are k-filters. We deduce that, for each countable ordinal , there exists a free filter of true additive class
(Baire's classification) and a free filter of true multiplicative class
for which the associated point-spaces are k-spaces but not
, the existence being true in the additive case for
. In particular, we answer negatively a question raised in J. Calbrix, C. R. Acad. Sci. Paris 305 (1987), 109--111.
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Additional Information
Jean Calbrix
Affiliation:
Laboratoire A.M.S. URA C.N.R.S. D1378, U.F.R. des Sciences, F76821 Mont Saint Aignan cedex, France
Email:
Jean.Calbrix@univ-rouen.fr
DOI:
https://doi.org/10.1090/S0002-9947-96-01635-2
Keywords:
Borel filters,
point-spaces,
k-spaces,
$\aleph _{0}$-spaces
Received by editor(s):
December 3, 1993
Article copyright:
© Copyright 1996
American Mathematical Society