Applications of the reflection functors in paratopological groups

We apply T-i-reflections for i = 0, 1, 2, 3, as well as the regular reflection defined by the author in [20] for the further study of paratopological and semitopological groups. We show that many topological properties are invariant and/or inverse invariant under taking T-i-refiections in paratopological groups. Using this technique, we prove that every a-compact paratopological group has the Knaster property and, hence, is of countable cellularity. We also prove that an arbitrary product of locally feebly compact paratopological groups is a Moscow space, thus generalizing a similar fact established earlier for products of feebly compact topological groups. The proof of the latter result is based on the fact that the functor T-2 of Hausdorff reflection 'commutes' with arbitrary products of semitopological groups. In fact, we show that the functors T-0 and T-1 also commute with products of semitopological groups, while the functors T-3 and Reg commute with products of paratopological groups. (C) 2015 Elsevier B.V. All rights reserved.