A countably compact topological group 𝐻 such that 𝐻×𝐻 is not countably compact

Hart, Klaas Pieter; van Mill, Jan

doi:10.1090/S0002-9947-1991-0982236-3

A countably compact topological group such that $H\times H$ is not countably compact

Authors: Klaas Pieter Hart and Jan van Mill
Journal: Trans. Amer. Math. Soc. 323 (1991), 811-821
MSC: Primary 54B10; Secondary 03E50, 22A05, 22C05, 54D30, 54G20
DOI: https://doi.org/10.1090/S0002-9947-1991-0982236-3
MathSciNet review: 982236
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Abstract: Using ${\mathbf{M}}{{\mathbf{A}}_{{\text{countable}}}}$ we construct a topological group with the properties mentioned in the title.

[CR] W. W. Comfort and Kenneth A. Ross, Pseudocompactness and uniform continuity in topological groups, Pacific J. Math. 16 (1966), 483–496. MR 207886
[vD] Eric K. van Douwen, The product of two countably compact topological groups, Trans. Amer. Math. Soc. 262 (1980), no. 2, 417–427. MR 586725, https://doi.org/10.1090/S0002-9947-1980-0586725-8
[Ru] Donald J. Albers and Constance Reid, An interview with Mary Ellen Rudin, College Math. J. 19 (1988), no. 2, 114–137. MR 944786, https://doi.org/10.2307/2686174
[We] William Weiss, Versions of Martin’s axiom, Handbook of set-theoretic topology, North-Holland, Amsterdam, 1984, pp. 827–886. MR 776638