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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Katetov's problem


Authors: Paul Larson and Stevo Todorcevic
Journal: Trans. Amer. Math. Soc. 354 (2002), 1783-1791
MSC (2000): Primary 54E35; Secondary 03E35, 03E65, 54E45
Published electronically: November 21, 2001
MathSciNet review: 1881016
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Abstract: In 1948 Miroslav Katetov showed that if the cube $X^{3}$ of a compact space $X$ satisfies the separation axiom T$_{5}$ then $X$ must be metrizable. He asked whether $X^{3}$ can be replaced by $X^{2}$ in this metrization result. In this note we prove the consistency of this implication.


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Additional Information

Paul Larson
Affiliation: Department of Mathematics, University of Toronto, Toronto M5S 3G3, Canada
Email: larson@math.toronto.edu

Stevo Todorcevic
Affiliation: C.N.R.S. (7056), Université Paris VII, 75251 Paris Cedex 05, France
Email: stevo@math.jussieu.fr

DOI: http://dx.doi.org/10.1090/S0002-9947-01-02936-1
PII: S 0002-9947(01)02936-1
Keywords: Compactness, metrizability, T$_{5}$, forcing
Received by editor(s): November 27, 2000
Received by editor(s) in revised form: July 30, 2001
Published electronically: November 21, 2001
Additional Notes: This work was done while the authors were in residence at the Mittag-Leffler Institute. We thank the Institute for its hospitality.
Article copyright: © Copyright 2001 American Mathematical Society