For any $X$, the product $X\times Y$ is homogeneous for some $Y$
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- by Vladimir V. Uspenskiĭ PDF
- Proc. Amer. Math. Soc. 87 (1983), 187-188 Request permission
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.References
- A. V. Arhangel′skiĭ, The structure and classification of topological spaces and cardinal invariants, Uspekhi Mat. Nauk 33 (1978), no. 6(204), 29–84, 272 (Russian). MR 526012
- Jan 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), no. 3, 597–600. MR 627701, DOI 10.1090/S0002-9939-1981-0627701-2
- Alan Dow and Jan van Mill, On nowhere dense ccc $P$-sets, Proc. Amer. Math. Soc. 80 (1980), no. 4, 697–700. MR 587958, DOI 10.1090/S0002-9939-1980-0587958-2
Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 87 (1983), 187-188
- MSC: Primary 54G20; Secondary 54B10
- DOI: https://doi.org/10.1090/S0002-9939-1983-0677259-9
- MathSciNet review: 677259