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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Varieties generated by countably compact Abelian groups


Authors: Dikran Dikranjan and Michael Tkachenko
Journal: Proc. Amer. Math. Soc. 130 (2002), 2487-2496
MSC (1991): Primary 22A05, 22B05, 54D25, 54H11; Secondary 54A35, 54B30, 54D30, 54H13
Published electronically: February 4, 2002
MathSciNet review: 1897476
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Abstract: We prove under the assumption of Martin's Axiom that every precompact Abelian group of size $\leq 2^{\aleph_0}$ belongs to the smallest class of groups that contains all Abelian countably compact groups and is closed under direct products, taking closed subgroups and continuous isomorphic images.


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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

Michael Tkachenko
Affiliation: Departamento de Matemáticas, Universidad Autónoma Metropolitana, México
Email: mich@xanum.uam.mx

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06354-2
PII: S 0002-9939(02)06354-2
Keywords: Countably compact, precompact, sequentially complete, variety of topological groups, Martin's Axiom
Received by editor(s): February 4, 2000
Received by editor(s) in revised form: March 21, 2001
Published electronically: February 4, 2002
Additional Notes: The first author was partially supported by Research Grant of the Italian MURST in the framework of the project “Nuove prospettive nella teoria degli anelli, dei moduli e dei gruppi abeliani" 2000
The second author was partially supported by the Mexican National Council of Sciences and Technology (CONACyT), grant no. 400200-5-3012PE. He also thanks the hosts for the hospitality and generous support during his visit to the Università di Udine, Italy in December, 1999
Communicated by: Alan Dow
Article copyright: © Copyright 2002 American Mathematical Society