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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 | References | Similar Articles | Additional Information

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

Stevo Todorcevic
Affiliation: C.N.R.S. (7056), Université Paris VII, 75251 Paris Cedex 05, France

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

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