Nondiscrete P-Groups Can be Reflexive

We present a series of examples of nondiscrete reflexive P-groups (i.e., groups in which all $G_δ$-sets are open) as well as noncompact reflexive $ω$-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.

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