Pseudocompact totally dense subgroups
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- by Dikran Dikranjan and Anna Giordano Bruno PDF
- Proc. Amer. Math. Soc. 136 (2008), 1093-1103 Request permission
Abstract:
It was shown by Dikranjan and Shakhmatov in 1992 that if a compact abelian group $K$ admits a proper totally dense pseudocompact subgroup, then $K$ cannot have a torsion closed $G_\delta$-subgroup; moreover this condition was shown to be also sufficient under LH. We prove in ZFC that this condition actually ensures the existence of a proper totally dense subgroup $H$ of $K$ that contains an $\omega$-bounded dense subgroup of $K$ (such an $H$ is necessarily pseudocompact). This answers two questions posed by Dikranjan and Shakhmatov (Proc. Amer. Math. Soc. 114 (1992), 1119–1129).References
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Additional Information
- Dikran Dikranjan
- Affiliation: Dipartimento di Matematica e Informatica, Università di Udine, Via delle Scienze 206, 33100 Udine, Italy
- Email: dikranja@dimi.uniud.it
- Anna Giordano Bruno
- Affiliation: Dipartimento di Matematica e Informatica, Università di Udine, Via delle Scienze 206, 33100 Udine, Italy
- Email: giordano@dimi.uniud.it
- Received by editor(s): May 8, 2006
- Received by editor(s) in revised form: October 23, 2006
- Published electronically: November 30, 2007
- Additional Notes: This work was partially supported by a PRIN2005 grant of the Italian MIUR and by funds of the PhD program at the Department of Mathematics of the University of Udine.
- Communicated by: Alexander N. Dranishnikov
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 1093-1103
- MSC (2000): Primary 22A05, 54H11; Secondary 22C05, 54D25
- DOI: https://doi.org/10.1090/S0002-9939-07-09099-5
- MathSciNet review: 2361886