Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Countably compact groups without non-trivial convergent sequences


Authors: M. Hrušák, J. van Mill, U. A. Ramos-García and S. Shelah
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
Published electronically: November 10, 2020
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2020): 22A05, 03C20, 03E05, 54H11

Retrieve articles in all journals with MSC (2020): 22A05, 03C20, 03E05, 54H11


Additional Information

M. Hrušák
Affiliation: Centro de Ciencias Matemáticas, Universidad Nacional Autónoma de México, Campus Morelia, Morelia, Michoacán, 58089 México
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
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
Email: shelah@math.huji.ac.il

DOI: https://doi.org/10.1090/tran/8222
Keywords: Products of countably compact groups, $p$-compact groups, ultrapowers, countably compact groups without convergent sequences
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
Article copyright: © Copyright 2020 American Mathematical Society