Hausdorff compactifications and zero-one measures II

Georgi D. Dimov, Gino Tironi


The notion of PBS-sublattice is introduced and, using it, a simplification of the results of [6] and of some results of [5] is obtained. Two propositions concerning Wallman-type compactifications are presented as well.


Hausdorff compactifications; zero-one measures on Boolean algebras; Maximal spectrum of distributive lattices; Efremovic proximities; Wallman-type compactifications

Full Text:



G. Bachman and R. Cohen, Regular Lattice Measures and Repleteness, Comm. on Pure and Applied Math. 26 (1973), 587-599.

H. Brandenburg and A. Mysior, Short proof of an internal characterization of complete regularity, Canad. Math. Bull. 27 (4) (1984), 461-462.

G. Bachman and P. Stratigos, On the Relation of Lattice Repleteness and C-Real Compactness, Indian J. Pure and Applied Math. 20 (11) (1989), 1043-1066.

R. Cohen, Lattice Measures and Topologies, Ann. Mat. Pura Appl. 109 (1976), 147-164.

G. Dimov and G. Tironi, Compactifications, A-Compactifi cations and Proximities, Ann. Mat. Pura Appl. 169 (1995), 87-108.

G. Dimov and G. Tironi, Hausdorff Compactifications and Zero-One Measures, Math. Proc. Camb. Phil. Soc. (2001) (to appear).

R. Engelking, General Topology, (PWN, Warszawa, 1977).

O. Frink, Compactifications and semi-normal spaces, Amer. J. Math. 86 (1964), 602-607.

P. T. Johnstone, Stone Spaces, Cambridge Studies in Advanced Math. no. 3 (Cambridge University Press, 1982).

J. Kerstan, Eine Charakterisierung der vollstandig regularen Raume, Math. Nachrichten 17 (1958), 27-46.

S. A. Naimpally and B. D. Warrack, Proximity Spaces, (Cambridge Univ. Press, 1970).

O. Njastad, On Wallman-type Compactifications, Math. Zeitschr 91 (1966), 267-276.

Y. M. Smirnoff, On proximity spaces, Mat. Sb. (Russian) 31 (1952), 543-574; Am. Math. Soc. Transl. (English translation) 38 Ser. 2, 5-35.

A. Sultan, Measure, compactification and representation, Can. J. Math. 30 (1) (1978), 54-65.

V. M. Ul0janov, Solution of a basic problem on compactifications of Wallman type, Soviet Math. Dokl. 18 (1977), 567-571.

H. Wallman, Lattices and topological spaces, Annals of Math. 39 (1938), 112-126.

Abstract Views

Metrics Loading ...

Metrics powered by PLOS ALM

Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147