Recent Progress in the Topological Theory of Semigroups and the Algebra of βS

Hindman, Neil; Strauss, Dona

doi:10.1016/b978-044450980-2/50009-1

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Introduction3

Solution To a Problem By Pestov1

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2007

2022

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Cited by 3 publications

(4 citation statements)

References 102 publications

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“…The following result is easily deduced (and known) from the comments immediately following Theorem 3.9 of [8].…”

Section: Introductionmentioning

confidence: 90%

On van Douwen spaces and retracts of $\beta {\mathbb{N}}$

Dow¹

2007

Math. Bohem.

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“…The following result is easily deduced (and known) from the comments immediately following Theorem 3.9 of [8].…”

Section: Introductionmentioning

confidence: 90%

On van Douwen spaces and retracts of $\beta {\mathbb{N}}$

Dow¹

2007

Math. Bohem.

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“…Quantitative improvements of Lemma 5.3 are known for non-compact, locally compact groups [23, Theorem 4.1], as well as for non-precompact, separable topological groups [10, Theorem 1.3] (see also [19,Theorem 3.8]).…”

Section: Solution To a Problem By Pestovmentioning

confidence: 99%

Concentration of invariant means and dynamics of chain stabilizers in continuous geometries

Schneider¹

2022

Preprint

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We prove a concentration inequality for invariant means on topological groups, namely for such adapted to a chain of amenable topological subgroups. The result is based on an application of Azuma's martingale inequality and provides a method for establishing extreme amenability. Building on this technique, we exhibit new examples of extremely amenable groups arising from von Neumann's continuous geometries. Along the way, we also answer a question by Pestov on dynamical concentration in direct products of amenable topological groups.

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“…[BH87]; since a strongly summable is strongly right maximal, its orbit is a van Douwen space, cf. [HS02].…”

Section: Introductionmentioning

confidence: 99%

“…[BH87]; since a strongly summable is strongly right maximal, its orbit is a van Douwen space, cf. [HS02]. This article will focus on union ultrafilters, studying the various kinds of union ultrafilters and as the main result constructing of a new kind of union ultrafilter answering a question of Andreas Blass.…”

Section: Introductionmentioning

confidence: 99%