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For any $ X$, the product $ X\times Y$ is homogeneous for some $ Y$

Author: Vladimir V. Uspenskiĭ
Journal: Proc. Amer. Math. Soc. 87 (1983), 187-188
MSC: Primary 54G20; Secondary 54B10
MathSciNet review: 677259
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Abstract: We prove that for every topological space $ X$ there exists a cardinal $ k$ and a nonempty subspace $ Y \subseteq {X^k}$ such that the product $ X \times Y$ is homogeneous. This answers a question of A. V. Arhangel'skiĭ.

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  • [A] A. V. Arhangel'skiĭ, Structure and classification of topological spaces and cardinal invariants, Russian Math. Surveys 33 (1978), 33-96. MR 526012 (80i:54005)
  • [vM] J. van Mill, A rigid space $ X$ for which $ X \times X$ is homogeneous; an application of infinite-dimensional topology, Proc. Amer. Math. Soc. 83 (1981), 597-600. MR 627701 (82h:54067)
  • [DvM] A. Dow and J. van Mill, On nowhere dense ccc $ P$-sets, Proc. Amer. Math. Soc. 80 (1980), 697-700. MR 587958 (82a:54032)

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Article copyright: © Copyright 1983 American Mathematical Society

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