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Katetov’s problem

2001; American Mathematical Society; Volume: 354; Issue: 5 Linguagem: Inglês

10.1090/s0002-9947-01-02936-1

1088-6850

Paul Larson, Stevo Todorčević,

advanced mathematical theories

In 1948 Miroslav Katětov showed that if the cube X 3 X^{3} of a compact space X X satisfies the separation axiom T 5 _{5} then X X must be metrizable. He asked whether X 3 X^{3} can be replaced by X 2 X^{2} in this metrization result. In this note we prove the consistency of this implication.