Hausdorff compactifications and zero-one measures II

Dimov, Georgi; Tironi, Gino

doi:10.4995/agt.2002.2106

Appl. Gen. Topol.

2002

DOI: 10.4995/agt.2002.2106

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Hausdorff compactifications and zero-one measures II

Georgi Dimov

Gino Tironi

Abstract: Abstract. 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.2000 AMS Classification: Primary 54D35, 28A60, 06D99; Secondary 54D80, 54E05, 06B99.

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A quasi-uniform characterization of Wallman type compactifications

Romaguera

Sánchez-Granero

2003

Studia Scientiarum Mathematicarum Hungarica

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A *-compactification of a T1 quasi-uniform space (X,U) is a compact T1 quasi-uniform space (Y,V) that has a T(V*)-dense subspace quasi-isomorphic to (X,U), where V* denotes the coarsest uniformity finer than V.In this paper we characterize all Wallman type compactifications of a T1 topological space in terms of the *-compactification of its point symmetric totally bounded transitive compatible quasi-uniformities. We deduce that the *-compactification of the Pervin quasi-uniformity of any normal T1 topological space X is exactly the Stone-Cech compactification of X. We also obtain a characterization of those Hausdorff compactifications of a given space, which are of Wallman type.

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A quasi-uniform characterization of Wallman type compactifications

Romaguera

Sánchez-Granero

2003

Studia Scientiarum Mathematicarum Hungarica

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Hausdorff compactifications and zero-one measures II

Cited by 1 publication

References 11 publications

A quasi-uniform characterization of Wallman type compactifications

A quasi-uniform characterization of Wallman type compactifications

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