A note on locally pathwise connected metric spaces
type: Item
instance of: scholarly article
title: A note on locally pathwise connected metric spaces
zbMATH Open document ID: 1153.54011
author: Paranjothi Pillay
author: Dharmanand Baboolal
published in: Applied Categorical Structures
publication date: 2008-09-10T00:00:00Z
review text: In 1932, Whyburn construced a new metric \(d^{*}\) from a given metric \(d\) by changing all the distances \(d(x,y)\) into the distances \(d^{*}(x,y)\), where \(d^{*}(x,y)\) is the infimum of the numbers \(d(C)\) for any connected set \(C\) containing \(x,\;y\), \(d(C)\) being the distances of \(C\). The author studies an analogous construction for locally pathwise connected metric spaces and gives an application of this by showing that the category of uniformly locally pathwise connected metric spaces and uniformly continuous maps is coreflective in the category of metric spaces and uniformly continuous maps.
reviewed by: Takemi Mizokami
Mathematics Subject Classification ID: 54E35
Mathematics Subject Classification ID: 54D05
Mathematics Subject Classification ID: 54B30
zbMATH DE Number: 5324372
zbMATH Keywords: metric space
zbMATH Keywords: locally pathwise connected
zbMATH Keywords: uniformly locally pathwise connected
MaRDI profile type: Publication
full work available at URL: s10485-007-9096-1
OpenAlex ID: W2029633703
cites work: Q4394844
cites work: A Certain Transformation on Metric Spaces
cites work: Q5605131
DOI: 10.1007/S10485-007-9096-1
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description: scientific article; zbMATH DE number 5324372