Countably compact groups without non-trivial convergent sequences
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- by M. Hrušák, J. van Mill, U. A. Ramos-García and S. Shelah PDF
- Trans. Amer. Math. Soc. 374 (2021), 1277-1296 Request permission
Abstract:
We construct, in ZFC, a countably compact subgroup of $2^\mathfrak c$ without non-trivial convergent sequences, answering an old problem of van Douwen. As a consequence we also prove the existence of two countably compact groups $\mathbb G_0$ and $\mathbb G_1$ such that the product $\mathbb G_0 \times \mathbb G_1$ is not countably compact, thus answering a classical problem of Comfort.References
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Additional Information
- M. Hrušák
- Affiliation: Centro de Ciencias Matemáticas, Universidad Nacional Autónoma de México, Campus Morelia, Morelia, Michoacán, 58089 México
- MR Author ID: 602083
- ORCID: 0000-0002-1692-2216
- Email: michael@matmor.unam.mx
- J. van Mill
- Affiliation: KdV Institute for Mathematics, University of Amsterdam, Science Park 105-107, P.O. Box 94248, 1090 GE Amsterdam, The Netherlands
- MR Author ID: 124825
- Email: j.vanMill@uva.nl
- U. A. Ramos-García
- Affiliation: Centro de Ciencias Matemáticas, Universidad Nacional Autónoma de México, Campus Morelia, Morelia, Michoacán, 58089 México
- Email: ariet@matmor.unam.mx
- S. Shelah
- Affiliation: Einstein Institute of Mathematics, Edmond J. Safra Campus, The Hebrew University of Jerusalem, Givat Ram, Jerusalem, 91904, Israel; and Department of Mathematics, Hill Center - Busch Campus, Rutgers, The State University of New Jersey, 110 Frelinghuysen Road, Piscataway, New Jersey 08854-8019
- MR Author ID: 160185
- ORCID: 0000-0003-0462-3152
- Email: shelah@math.huji.ac.il
- Received by editor(s): December 3, 2019
- Received by editor(s) in revised form: June 8, 2020, and June 13, 2020
- Published electronically: November 10, 2020
- Additional Notes: The research of the first author was supported by a PAPIIT grant IN100317 and CONACyT grant A1-S-16164. The third named author was partially supported by the PAPIIT grants IA100517 and IN104419. Research of the fourth author was partially supported by European Research Council grant 338821. Paper 1173 on the fourth author’s list
- © Copyright 2020 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 374 (2021), 1277-1296
- MSC (2020): Primary 22A05, 03C20; Secondary 03E05, 54H11
- DOI: https://doi.org/10.1090/tran/8222
- MathSciNet review: 4196393