Nearness, subfitness and sequential regularity
type: Item
instance of: scholarly article
title: Nearness, subfitness and sequential regularity
zbMATH Open document ID: 0978.54001
DOI: 10.1023/A:1008786312677
author: Horst Herrlich
author: A. Pultr
published in: Applied Categorical Structures
publication date: 2001-02-11T00:00:00Z
review text: In the point-free context, the structure of nearness has been studied so far only in the regular case. The authors are concerned with the question as to how far beyond regularity one can go, that is, what is the weakest separation property under which an admissible nearness makes a reasonable sense. The answer is subfitness. Main theorem: The following statements on a frame \(L\) are equivalent: (i) Each sublocale of \(L\) quasi-admits a nearness; (ii) \(L\) is hereditarily subfit; (iii) \(L\) is sequentially regular; (iv) Each congruence on \(L\) is uniquely determined by the class containing 1. Finally, the authors compare the sequential regularity with more common separation axioms.
Mathematics Subject Classification ID: 54A05
Mathematics Subject Classification ID: 06D22
Mathematics Subject Classification ID: 06D10
Mathematics Subject Classification ID: 54E17
Mathematics Subject Classification ID: 54D10
zbMATH DE Number: 1563337
zbMATH Keywords: nearness space
zbMATH Keywords: nearness frame
zbMATH Keywords: subfit frame
zbMATH Keywords: regular
reviewed by: Bohumil František Šmarda
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1563337