Zero dimensionality of the Cech-Stone compactification of an approach space

Given a Hausdorff zero-dimensional approach space X with gauge g, we investigate its tech-Stone compactification beta* (X) and characterise zero-dimensionality of the compactification. This is done by comparing beta*(X) to the Banaschewski compactification zeta*(X). The notion of strongly zero-dimensional is introduced. For a Hausdorff zero-dimensional approach space X this property is shown to be equivalent to beta* (X) = zeta* (X). When strongly zero-dimensional is combined with approach normal, then this yields a property which we call d(M)-approach normality. Both strongly zero-dimensional and approach normal are implied by d(M)-approach normal. For topological approach spaces we recover the well known relations between ultra normal, normal and strongly zero-dimensional. A zero-dimensional metric approach space is ultrametric and even the strong property, d(M)-approach normality, is fulfilled by any ultrametric space. (C) 2019 Elsevier B.V. All rights reserved.

Publication year:2020

Keywords:A1 Journal article

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BOF-publication weight:0.5

CSS-citation score:1

Authors from:Higher Education

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