Metric spaces with discrete topological fundamental group (Q861945)
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scientific article; zbMATH DE number 5121456
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Metric spaces with discrete topological fundamental group |
scientific article; zbMATH DE number 5121456 |
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Metric spaces with discrete topological fundamental group (English)
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2 February 2007
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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 \(X\).
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topological fundamental group
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semilocally simply connected
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