Abstract colorings, games and ultrafilters

Autor:	Piotr Szewczak
Rok vydání:	2021
Předmět:	Primary: 05D10 54D20 54C35 Secondary: 16W22 Mathematics::Logic General Topology (math.GN) FOS: Mathematics Mathematics - Combinatorics Mathematics::General Topology Geometry and Topology Combinatorics (math.CO) Mathematics - General Topology
DOI:	10.48550/arxiv.2107.02830
Popis:	The main result provide a common generalization for Ramsey-type theorems concerning finite colorings of edge sets of complete graphs with vertices in infinite semigroups. We capture the essence of theorems proved in different fields: for natural numbers due to Milliken--Tylor, Deuber--Hindman, Bergelson--Hindman, for combinatorial covering properties due to Scheepers and Tsaban, and local properties in function spaces due to Scheepers. To this end, we use idempotent ultrafilters in the \v{C}ech--Stone compactifications of discrete infinite semigroups and topological games. The research is motivated by the recent breakthrough work of Tsaban about colorings and the Menger covering property. Comment: 21 pages
Databáze:	OpenAIRE
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