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.

Z. Feng and R.W. Heath proved that any separable linearly ordered space (LOTS) which is a cancellative topological semigroup must be metrizable. In this note, we show that the same holds more generally for CCC LOTS by proving that no Souslin line admits a continuous cancellative binary operation. We also show that no Lindelöf Aronszajn line admits such an operation.

Let X, Y be compact convex sets such that every extreme point of X and Y is a weak peak point and both extX and extY are Lindelöf spaces. We prove that, if there exists an isomorphism T : Ac(X) → Ac(Y ) with ‖T‖ · ‖T‖ < 2, then extX is homeomorphic to extY . This generalizes results of H.B. Cohen and C.H. Chu.

The concepts of γ-compactness, countable γ-compactness, the γ-Lindelöf property are introduced in L-topological spaces by means of γ-open L-sets and their inequalities when L is a complete DeMorgan algebra. These definitions do not rely on the structure of the basis lattice L and no distributivity in L is required.