Cardinal invariants and R-factorizability in paratopological groups

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 | ⩽ 2 i b ( 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 R 2 -factorizable (resp. R 3 -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 R 2 -factorizable (resp. R 3 -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 R 2 -factorizable (resp. R 3 -factorizable), which gives a partial answer to the question posed by M. Sanchis and M.G. Tkachenko (2010) [17] .