Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

A non-metrizable space whose countable power is $\sigma$ -metrizable

Author(s): Gary Gruenhage
Journal: Proc. Amer. Math. Soc. 125 (1997), 1881-1883.
MSC (1991): Primary 54E35, 54B10, 54B05
MathSciNet review: 1415587
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Abstract: We answer a question of A.V. Arhangel'skii by finding a non-metrizable space $X$ such that $X^{\omega }$ is the countable union of metrizable spaces.

References:

[1]: Z. Balogh, G. Gruenhage, and V.V. Tkachuk, Additivity of metrizability and related properties, Topology and Appl., to appear.
[2]: M.G. Tkacenko, Ob odnom svoistve bicompactov (On a property of compact spaces), Seminar po obshchei topologii (A seminar on general topology), Moscow State Univ. P.H., Moscow, 1981, pp. 149-156.
[3]: V.V. Tkachuk, Finite and countable additivity of topological properties in nice spaces, Trans. Amer. Math. Soc. 341 (2) (1994), 585-601. MR 94d:54014

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