The continuous d-open homomorphism images and subgroups of [formula omitted]-factorizable paratopological groups

Abstract

In this paper, we prove the following results: (1) Let f:G→H be a continuous d-open surjective homomorphism; if G is an R-factorizable paratopological group, then so is H. This improves a result by Peng and Zhang [4, Theorem 1.7], and (2) let G be a regular (so G is completely regular by a theorem of Banakh and Ravsky) R-factorizable paratopological group; then every subgroup H of G is R-factorizable if and only if H is z-embedded in G. This result gives a partial answer to a question of M. Sanchis and M. Tkachenko [8, Problem 5.3].