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Hausdorff compactifications and zero-one measures

Published online by Cambridge University Press:  26 November 2001

GEORGI D. DIMOV  and
GINO TIRONI
GEORGI D. DIMOV
Affiliation:
Department of Mathematics and Computer Science, University of Sofia, Blvd J. Bourchier 5, 1126 Sofia, Bulgaria. e-mail: [email protected]
GINO TIRONI
Affiliation:
Department of Mathematical Sciences, University of Trieste, Via Alfonso Valerio 12/1, 34127 Trieste, Italy
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Abstract

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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 131 , Issue 3 , November 2001 , pp. 495 - 505
Copyright
© 2001 Cambridge Philosophical Society

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