Nondiscrete P-Groups Can be Reflexive

Abstract

We present a series of examples of nondiscrete reflexive P-groups (i.e., groups in which all $G_{\delta }$-sets are open) as well as noncompact reflexive $\omega$-bounded groups (in which the closure of every countable set is compact). Our main result implies that every product of feathered (equivalently, almost metrizable) Abelian groups equipped with the P-modified topology is a reflexive group. In particular, every compact Abelian group with the P-modified topology is reflexive. This answers a question posed by S. Hernández and P. Nickolas and solves a problem raised by Ardanza-Trevijano, Chasco, Dom\'ınguez, and Tkachenko.

29 pages

Cited by in corpus (1)

• Reflexivity in precompact groups and extensions