Let C denote any of the following cardinal characteristics of Boolean algebras: incomparability, spread, character, π-character, hereditary Lindelöf number, hereditary density. It is shown to be consistent that there exists a sequence 〈Bi : i < κ〉 of Boolean algebras and an ultrafilter D on κ such that

We prove that if a paratopological group G is a continuous image of an arbitrary product of regular Lindelöf Σ-spaces, then it is R-factorizable and has countable cellularity. If in addition, G is regular, then it is totally ω-narrow and satisfies celω(G) ≤ ω, and the Hewitt–Nachbin completion of G is again an R-factorizable paratopological group.