Metric spaces with discrete topological fundamental group
type: Item
instance of: scholarly article
title: Metric spaces with discrete topological fundamental group
zbMATH Open document ID: 1111.55014
author: Paul Fabel
published in: Topology and its Applications
publication date: 2007-02-02T00:00:00Z
review text: It was asserted in Theorem 5.1 [\textit{D. K. Biss}, Topology Appl. 124, No. 3, 355--371 (2002; Zbl 1016.57002)] that the topological fundamental group \(\pi_1^{\text{top}}(X,p)\) of a metric space is discrete if and only if \(X\) is semilocally simply connected. In this brief note, the author gives a counterexample to this theorem and fixes it by adding the condition of locally path connectedness on \(X\).
Mathematics Subject Classification ID: 55U40
Mathematics Subject Classification ID: 57M05
zbMATH DE Number: 5121456
zbMATH Keywords: topological fundamental group
zbMATH Keywords: semilocally simply connected
reviewed by: J. Remedios
MaRDI profile type: Publication
full work available at URL: j.topol.2006.08.004
OpenAlex ID: W2083148969
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DOI: 10.1016/J.TOPOL.2006.08.004
description: scientific article; zbMATH DE number 5121456