Pseudocompact topological group refinements of maximal weight
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- by W. W. Comfort and Jorge Galindo PDF
- Proc. Amer. Math. Soc. 131 (2003), 1311-1320 Request permission
Abstract:
It is known that a compact metrizable group admits no proper pseudocompact topological group refinement. The authors show, in contrast, that every (Hausdorff) pseudocompact Abelian group $G=(G,\mathcal {T})$ of uncountable weight $\alpha$, satisfying any of the following conditions, admits a pseudocompact group refinement of maximal weight (that is, of weight $2^{|G|}$):
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[(i)] $G$ is compact;
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[(ii)] $G$ is torsion-free with $\alpha \leq |G|=|G|^\omega$;
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[(iii)] [GCH] $G$ is torsion-free.
Remark. (i) answers a question posed by Comfort and Remus [Math. Zeit- schrift 215 (1994), 337–346].
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Additional Information
- W. W. Comfort
- Affiliation: Department of Mathematics, Wesleyan University, Middletown, Connecticut 06459
- Email: wcomfort@wesleyan.edu
- Jorge Galindo
- Affiliation: Departamento de Matemáticas, Universitat Jaume I, 8029-AP Castellón, Spain
- MR Author ID: 615222
- Email: jgalindo@mat.uji.es
- Received by editor(s): August 21, 2000
- Received by editor(s) in revised form: December 4, 2001
- Published electronically: September 5, 2002
- Additional Notes: This paper is based on work completed during the visit of the second-listed author to the Department of Mathematics of Wesleyan University, during the Fall Term of the academic year 1998-1999
The work of the second author was supported in part by Spanish DGES, grant number BFM 2000-0913. The second author acknowledges with thanks hospitality and support received from the Department of Mathematics of Wesleyan University - Communicated by: Alan Dow
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 1311-1320
- MSC (2000): Primary 22A05, 54H11
- DOI: https://doi.org/10.1090/S0002-9939-02-06650-9
- MathSciNet review: 1948125