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

Author: 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 [Enhancements On Off] (What's this?)

  • [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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Additional Information

Gary Gruenhage
Affiliation: Department of Mathematics, Auburn University, Alabama 36849

Received by editor(s): March 6, 1996
Communicated by: Franklin D. Tall
Article copyright: © Copyright 1997 American Mathematical Society

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