Precompact noncompact reflexive abelian groups

Abstract

We present a series of examples of precompact, noncompact, reflexive topological Abelian groups. Some of them are pseudocompact or even countably compact, but we show that there exist precompact non-pseudocompact reflexive groups as well. It is also proved that every pseudocompact Abelian group is a quotient of a reflexive pseudocompact group with respect to a closed reflexive pseudocompact subgroup.

Cited by in corpus (2)

• Reflexivity in precompact groups and extensions
• Selectively pseudocompact groups without non-trivial convergent sequences