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Solution to Generalized Borsuk Problem in Terms of the Gromov–Hausdorff Distances to Simplexesстатья
- Авторы: Ivanov Alexander O., Tuzhilin Alexey A.
- Журнал: ArXiv e-prints, arXiv:1906.10574
- Год издания: 2019
- Аннотация: In the present paper the following Generalized Borsuk Problem is studied: Can a given bounded metric space X be partitioned into a given number m (probably an infinite one) of subsets, each of which has a smaller diameter than X? We give a complete answer to this question in terms of the Gromov-Hausdorff distance from X to a simplex of cardinality m and having a diameter less than X. Here a simplex is a metric space, all whose non-zero distances are the same.
- Добавил в систему: Тужилин Алексей Августинович