Cauchy complete nearness spaces
type: Item
instance of: scholarly article
title: Cauchy complete nearness spaces
zbMATH Open document ID: 0968.54021
DOI: 10.1023/A:1008709313586
author: S. S. Hong
author: Young Kyoung Kim
published in: Applied Categorical Structures
publication date: 2001-09-16T00:00:00Z
review text: Every nearness space has a strict complete regular nearness completion. For regular nearness spaces this provides a reflection, but for \(N_2\)-spaces the strict completion may fail to be a reflection. The authors improve this situation by introducing the concepts of Cauchy complete nearness spaces, Cauchy maps and Cauchy completions (as suitable subspaces of the strict completion), and by demonstrating that Cauchy completions provide a reflection in the category of \(N_2\)-spaces and Cauchy maps.
reviewed by: Horst Herrlich
Mathematics Subject Classification ID: 54E17
Mathematics Subject Classification ID: 54D35
Mathematics Subject Classification ID: 18A40
zbMATH DE Number: 1563347
zbMATH Keywords: nearness space
zbMATH Keywords: completion
zbMATH Keywords: regular Cauchy filter
zbMATH Keywords: Cauchy completion
zbMATH Keywords: Cauchy map
MaRDI profile type: Publication
full work available at URL: a:1008709313586
OpenAlex ID: W4252533137
description: scientific article; zbMATH DE number 1563347