The cactus tree of a metric space
We extend the cactus theorem of Dinitz, Karzanov, Lomonosov to metric spaces. In particular we show that if X is a separable continuum which is not separated by n-1 points then the set of all n-tuples of points separating X can be encoded by an R-tree.
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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2011
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| _version_ | 1797068371962888192 |
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| author | Papasoglu, P Swenson, E |
| author_facet | Papasoglu, P Swenson, E |
| author_sort | Papasoglu, P |
| collection | OXFORD |
| description | We extend the cactus theorem of Dinitz, Karzanov, Lomonosov to metric spaces. In particular we show that if X is a separable continuum which is not separated by n-1 points then the set of all n-tuples of points separating X can be encoded by an R-tree. |
| first_indexed | 2024-03-06T22:09:49Z |
| format | Journal article |
| id | oxford-uuid:516c9cce-6843-48b3-8e07-ac9bccc1c6a9 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T22:09:49Z |
| publishDate | 2011 |
| record_format | dspace |
| spelling | oxford-uuid:516c9cce-6843-48b3-8e07-ac9bccc1c6a92022-03-26T16:19:26ZThe cactus tree of a metric spaceJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:516c9cce-6843-48b3-8e07-ac9bccc1c6a9EnglishSymplectic Elements at Oxford2011Papasoglu, PSwenson, EWe extend the cactus theorem of Dinitz, Karzanov, Lomonosov to metric spaces. In particular we show that if X is a separable continuum which is not separated by n-1 points then the set of all n-tuples of points separating X can be encoded by an R-tree. |
| spellingShingle | Papasoglu, P Swenson, E The cactus tree of a metric space |
| title | The cactus tree of a metric space |
| title_full | The cactus tree of a metric space |
| title_fullStr | The cactus tree of a metric space |
| title_full_unstemmed | The cactus tree of a metric space |
| title_short | The cactus tree of a metric space |
| title_sort | cactus tree of a metric space |
| work_keys_str_mv | AT papasoglup thecactustreeofametricspace AT swensone thecactustreeofametricspace AT papasoglup cactustreeofametricspace AT swensone cactustreeofametricspace |