Symmetric monochromatic subsets in colorings of the Lobachevsky plane

Taras Banakh ⁽¹⁾, Artem Dudko ⁽²⁾, Dusan Repovs ^{(3) (4)}

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) 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

• [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
• Partition
• central symmetry
• monochromatic set
• Borel piece
• Lobachevsky plane
• Poincare model
• Borel k-partition
• coloring

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