Hausdorff Compactifications and Zero-One Measures
by
Gino Tironi
Department of Mathematical Sciences, University of Trieste
Coauthors: Georgi Dimov (University of Sofia)

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. Using the technique developed in previous papers of the authors, we find for any Tychonoff space X a Boolean algebra B_X and a set L_X of sublattices of B_X having the following property: for any Hausdorff compactification cX of X there exists a (unique) L_cX in L_X such that the maximal spectrum of L_cX and the space of all u-regular zero-one measures on the Boolean subalgebra b(L_cX) of B_X, generated by L_cX, are Hausdorff compactifications of X equivalent to cX.

Date received: July 1, 2000