Countably compact groups without non-trivial convergent sequences

M. Hrušák; J. van Mill; U. A. Ramos-García; S. Shelah

doi:10.1090/tran/8222

Countably compact groups without non-trivial convergent sequences

M. Hrušák
, J. van Mill
, U. A. Ramos-García
, S. Shelah

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

We construct, in ZFC, a countably compact subgroup of 2^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 G₀ and G₁ such that the product G₀ × G₁ is not countably compact, thus answering a classical problem of Comfort.

Original language	English
Pages (from-to)	1277-1296
Number of pages	20
Journal	Transactions of the American Mathematical Society
Volume	374
Issue number	2
DOIs	https://doi.org/10.1090/tran/8222
State	Published - Feb 2021

Bibliographical note

Publisher Copyright:
© 2020 American Mathematical Society

Keywords

Countably compact groups without convergent sequences
P-compact groups
Products of countably compact groups
Ultrapowers

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10.1090/tran/8222

Cite this

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Countably compact groups without non-trivial convergent sequences

Abstract

Bibliographical note

Keywords

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