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Precompact noncompact reflexive Abelian groups
-
Sergio Ardanza-Trevijano
,
María Jesús Chasco
Published/Copyright:
February 25, 2012
Abstract.
We study Pontryagin reflexivity in the class of precompact topological Abelian groups. We find reflexive groups among precompact not pseudocompact and among pseudocompact not compact groups. Making use of Martin's axiom we give an example of a reflexive countably compact not compact Abelian group. We also prove that every pseudocompact Abelian group is a quotient of a reflexive pseudocompact group with respect to a closed reflexive pseudocompact subgroup.
Keywords.: Precompact group; pseudocompact group; countably compact group; -embedded subgroup; Pontryagin dual; Pontryagin reflexive group
Received: 2010-01-29
Revised: 2010-03-26
Published Online: 2012-02-25
Published in Print: 2012-March
© 2012 by Walter de Gruyter Berlin Boston
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Keywords for this article
Precompact group;
pseudocompact group;
countably compact group;
-embedded subgroup;
Pontryagin dual;
Pontryagin reflexive group
Articles in the same Issue
- Masthead
- Uniform weighted estimates for oscillatory singular integrals
- Solutions of the linear Boltzmann equation and some Dirichlet series
- Confluence and combinatorics in finitely generated unital lattice-ordered abelian groups
- Periodic flat resolutions and periodicity in group (co)homology
- Precompact noncompact reflexive Abelian groups
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Free profinite
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Cellular covers for
- Time changes of local Dirichlet spaces by energy measures of harmonic functions
- A construction of a universal connection
- Finitely generated algebraic structures with various divisibility conditions
- Quasiprojective varieties admitting Zariski dense entire holomorphic curves
- Conservativeness of non-symmetric diffusion processes generated by perturbed divergence forms
