Abstract
In this paper, cardinal invariants and R-factorizability in paratopological groups are studied. The main results are that (1) w(G)=ib(G⁎)×χ(G) holds for every paratopological group G; (2) every paratopological group G satisfies |G|⩽2ib(G⁎)ψ(G); (3) nw(G)=Nag(G)×ψ(G) is valid for every completely regular paratopological group G; (4) a completely regular paratopological group G is R2-factorizable (resp. R3-factorizable) if and only if it is a totally ω-narrow paratopological group with property ω-QU and Hs(G)⩽ω (resp. Ir(G)⩽ω); (5) if G is a completely regular R2-factorizable (resp. R3-factorizable) paratopological group and p:G→K an open homomorphism onto a paratopological group K such that p−1(e) is countably compact, then K is R2-factorizable (resp. R3-factorizable), which gives a partial answer to the question posed by M. Sanchis and M.G. Tkachenko (2010) [17].
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