On complete spaces for the Carathéodory distance (Q1335482)
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scientific article; zbMATH DE number 650746
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On complete spaces for the Carathéodory distance |
scientific article; zbMATH DE number 650746 |
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On complete spaces for the Carathéodory distance (English)
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10 October 1994
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The authors construct a 1-dimensional complex analytic space with the following properties. The Carathéodory distance and the inner Carathéodory distance (defined using piecewise continuously differentiable paths) both induce the underlying topology. The inner Carathéodory distance is strongly complete in the sense that all closed balls are compact, but the Carathéodory distance is not even Cauchy complete.
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Carathéodory distance
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inner Carathéodory distance
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