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Indivisible ultrametric spaces |
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| Authors: | Christian Delhommé ,Maurice Pouzet |
| Affiliation: | a E.R.M.I.T., Département de Mathématiques et d'Informatique, Université de La Réunion, 15, avenue René Cassin, BP 71551, 97715 Saint-Denis Messag, cedex 9, La Réunion, France b University of Calgary, Department of Mathematics and Statistics, Calgary, Alberta, Canada T2N 1N4 c PCS, Université Claude-Bernard Lyon1, Domaine de Gerland-bât, Recherche [B], 50 avenue Tony-Garnier, F69365 Lyon cedex 07, France |
| Abstract: | A metric space is indivisible if for any partition of it into finitely many pieces one piece contains an isometric copy of the whole space. Continuing our investigation of indivisible metric spaces [C. Delhommé, C. Laflamme, M. Pouzet, N. Sauer, Divisibility of countable metric spaces, European J. Combin. 28 (2007) 1746-1769], we show that a countable ultrametric space is isometrically embeddable into an indivisible ultrametric space if and only if it does not contain a strictly increasing sequence of balls. |
| Keywords: | 54E35 54E40 03C13 |
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