Compactifications, A-compactifications and proximities

Hausdorff compactifications and zero-one measures II

“…By Lemma 3.15, there exists a PB-sublattice L of L(X) such that p(L ) = L. In Proposition 2.12 of [5] we show that the relation δ L generated by L , defined in the same way as we define here the relation δ L , is a proximity on the space (X, T ). Hence, δ L is such one, as well.…”

“…Hence, in general, not every Hausdorff compactification of a Tychonoff space X can be obtained as a maximal spectrum of a normal Wallman base of X. In our paper [6], using the notion of PB-sublattice introduced in [5], we answered affirmatively two natural questions. The first one was: Problem 1.1.…”

“…Hence, δ L is such one, as well. This fact can be also obtained directly, modifying the proof of Proposition 2.12 of [5].…”

“…Let us remark that in [5] the notion of "PB-sublattice" was introduced with the redundant (as Proposition 3.5 shows now) requirement that a PB-sublattice is (by definition) a sublattice of L(Coz(X)).…”

“…In this paper we introduce the notion of PBS-sublattice and, using it, we obtain a simplification of the results of [6] and of some results of [5]. We also present the notion of PB-sublattice in a simpler but equivalent form.…”