Reflexivity in precompact groups and extensions
Scholar | Other documents of the author: Galindo Pastor, Jorge; Tkachenko, Mikhail; Bruguera, Montserrat; Hernández, Constancio
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TitleReflexivity in precompact groups and extensions
We establish some general principles and find some counter-examples concerning the Pontryagin reflexivity of precompact groups and P-groups. We prove in particular that: (1) A precompact Abelian group G ... [+]
We establish some general principles and find some counter-examples concerning the Pontryagin reflexivity of precompact groups and P-groups. We prove in particular that: (1) A precompact Abelian group G of bounded order is reflexive iff the dual group G∧G∧ has no infinite compact subsets and every compact subset of G is contained in a compact subgroup of G. (2) Any extension of a reflexive P-group by another reflexive P-group is again reflexive. We show on the other hand that an extension of a compact group by a reflexive ω-bounded group (even dual to a reflexive P-group) can fail to be reflexive. We also show that the P-modification of a reflexive σ-compact group can be non-reflexive (even if, as proved in , the P-modification of a locally compact Abelian group is always reflexive). [-]
Bibliographic citationGALINDO, J., et al. Reflexivity in precompact groups and extensions. Topology and its Applications, 2014, 163: 112-127.
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