It is well known that the Wallman-type compactifications of a Tychonoff space
X can be obtained as spaces of all regular zero-one measures on suitable lattices of
subsets of X (see [1, 2, 4, 12]).
Using the technique developed in [5, 6], we find for
any Tychonoff space X a Boolean algebra [Bscr ]X
and a set [Lscr ]X of sublattices of [Bscr ]X
having the following property: for any Hausdorff compactification cX of X there
exists a (unique) LcX ∈ [Lscr ]X
such that the maximal spectrum of LcX and the space of
all u-regular zero-one measures on the Boolean subalgebra b(LcX)
of [Bscr ]X, generated by LcX, are Hausdorff compactifications
of X equivalent to cX. Let us give more details now.