For any , the product
is homogeneous for some
Author:
Vladimir V. Uspenskiĭ
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
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Abstract | References | Similar Articles | Additional Information
Abstract: We prove that for every topological space there exists a cardinal
and a nonempty subspace
such that the product
is homogeneous. This answers a question of A. V. Arhangel'skiĭ.
- [A] 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
- [vM] Jan van Mill, A rigid space 𝑋 for which 𝑋×𝑋 is homogeneous; an application of infinite-dimensional topology, Proc. Amer. Math. Soc. 83 (1981), no. 3, 597–600. MR 627701, https://doi.org/10.1090/S0002-9939-1981-0627701-2
- [DvM] Alan Dow and Jan van Mill, On nowhere dense ccc 𝑃-sets, Proc. Amer. Math. Soc. 80 (1980), no. 4, 697–700. MR 587958, https://doi.org/10.1090/S0002-9939-1980-0587958-2
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1983-0677259-9
Article copyright:
© Copyright 1983
American Mathematical Society