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Metric spaces where geodesics are never unique
This article concerns a class of metric spaces, which we call multigeodesic spaces, where between any two distinct points there exist multiple distinct minimising geodesics. We provide a simple characterisation of multigeodesic normed spaces and deduce that (C([0,1]), ǀǀ٠ǀǀ1) is an example of such a...
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| Format: | Default Article |
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2023
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| Online Access: | https://hdl.handle.net/2134/22592161.v1 |
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| Summary: | This article concerns a class of metric spaces, which we call multigeodesic spaces, where between any two distinct points there exist multiple distinct minimising geodesics. We provide a simple characterisation of multigeodesic normed spaces and deduce that (C([0,1]), ǀǀ٠ǀǀ1) is an example of such a space, but that finite-dimensional normed spaces are not. We also investigate what additional features are possible in arbitrary metric spaces which are multigeodesic. |
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