Hausdorff compactifications and zero-one measures II


  • Georgi D. Dimov University of Sofia
  • Gino Tironi University of Trieste



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


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.


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Author Biographies

Georgi D. Dimov, University of Sofia

Department of Mathematics and Computer Science

Blvd. J. Bourchier 51126 Soa, Bulgaria

Gino Tironi, University of Trieste

Department of Mathematical Sciences

Via A. Valerio 12/134127 Trieste, Italy


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.




How to Cite

G. D. Dimov and G. Tironi, “Hausdorff compactifications and zero-one measures II”, Appl. Gen. Topol., vol. 3, no. 1, pp. 1–11, Apr. 2002.



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