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Title
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Zero dimensionality of the Cech-Stone compactification of an approach space
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Author
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Abstract
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| 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. |
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Language
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English
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Source (journal)
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Topology and its applications. - Amsterdam
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Publication
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Amsterdam
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2020
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ISSN
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0166-8641
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DOI
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10.1016/J.TOPOL.2019.106973
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Volume/pages
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273
(2020)
, p. 1-16
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Article Reference
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106973
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ISI
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000521514200016
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Medium
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E-only publicatie
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Full text (Publisher's DOI)
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Full text (publisher's version - intranet only)
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