R-factorizable, simply sm-factorizable paratopological groups and their quotients

摘要

In this article, we study R-factorizability (simple sm-factorizability) in paratopological groups. We show that if H is a continuous open homomorphic image of an R-factorizable paratopological group, then H is R-factorizable. This gives an affirmative answer to a problem posed by M. Sanchis and M. Tkachenko in [12, Problem 5.2]. We also prove that every weakly Lindelof totally omega-narrow paratopological group is simply sm-factorizable.We show that if a paratopological group H is a continuous homomorphic image of an R-factorizable paratopological group and H is weakly Lindelof (or first-countable), then H is simply sm-factorizable. This gives a partial answer to a problem posed by A.V. Arhangel'skii and M. Tkachenko in [1, Problem 7.8]. (C) 2019 Elsevier B.V. All rights reserved.