Ultrafilters: Where topological dynamics = algebra = combinatorics. (English) Zbl 0856.54042

Blass, Andreas

Topol. Proc. 18, 33-56 (1993).

Summary: We survey some connections between topological dynamics, semigroups of ultrafilters, and combinatorics. As an application, we give a proof, based on ideas of V. Bergelson and N. Hindman [Trans. Am. Math. Soc. 320, 293-320 (1990; Zbl 0725.22001)], of the Hales-Jewett partition theorem [A. W. Hales and R. I. Jewett, ibid. 106, 222-229 (1963; Zbl 0113.14802)].

MSC:

54H20	Topological dynamics (MSC2010)
54D80	Special constructions of topological spaces (spaces of ultrafilters, etc.)
05E99	Algebraic combinatorics
54A25	Cardinality properties (cardinal functions and inequalities, discrete subsets)
05D10	Ramsey theory

Citations:

Zbl 0725.22001; Zbl 0113.14802