Monochrome Symmetric Subsets in 2-Colorings of Groups
نویسندگان
چکیده
منابع مشابه
Monochrome Symmetric Subsets in 2-Colorings of Groups
A subset A of a group G is called symmetric with respect to the element g ∈ G if A = gA−1g. It is proved that in any 2-coloring, every infinite group G contains monochrome symmetric subsets of arbitrarily large cardinality < |G|. A topological space is called resolvable if it can be partitioned into two dense subsets [8]. In [4] W. Comfort and J. van Mill proved that each nondiscrete topologica...
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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. It follows from [B1] (see also [BP1, Theorem 1]) that for each partition of the n-dimensional space R into n pieces one of the pieces contains an unbounded centrally symmetric subset. On the other hand, R admits a partition...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2003
ISSN: 1077-8926
DOI: 10.37236/1721