Cardinal invariants in quasitopological groups

Abstract

For a given paratopological group (H,τ), the quasitopological group Q2(H) with a weaker topology than τ were investigated and some problems were posed by I. Sánchez and M. Tkachenko. In this note, we give partial answers to two of the problems. Some cardinal inequalities are obtained: (1) if H is a quasitopological group, then ib(H)≤e(H); (2) if H is a paratopological group, then ib(Q3(H))≤wl(H); (3) if H is a saturated semitopological group, then ib(H)≤s(H); (4) if H is a semitopological group, then ib(Q3(H))≤c(H).