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Symmetric monochromatic subsets in colorings of the Lobachevsky plane

Taras Banakh 1 Artem Dudko 2 Dusan Repovs 3, 4
1 Department of Mathematics [Lviv]
2 University of Toronto
3 FMF - Faculty of Mathematics and Physics [Ljubljana]
4 Faculty of Education [Ljubljana]
Abstract : We prove that for each partition of the Lobachevsky plane into finitely many Borel pieces one of the cells of the partition contains an unbounded centrally symmetric subset.
Keywords : Partition central symmetry monochromatic set Borel piece Lobachevsky plane Poincare model Borel k-partition coloring
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Taras Banakh, Artem Dudko, Dusan Repovs. Symmetric monochromatic subsets in colorings of the Lobachevsky plane. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2010, 12 (1), pp.12-20. ⟨hal-00990434⟩

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