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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We prove under the assumption of Martin's Axiom that every precompact Abelian group of size 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

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