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<p>We investigate a notion of largeness introduced by Bergelson and Robertson. Given a notion <i>R</i> of largeness in a semigroup, a set is an <i>almost R</i> set if it differs from an <i>R</i> set by a set with Banach density zero. We investigate almost large sets for several notions of largeness, establishing the exact relationships among many of these sets for subsets of the set <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {N}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">N</mi> </math></EquationSource> </InlineEquation> of positive integers.</p>

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Almost large subsets of a semigroup

  • 期刊论文

  • 发表日期：

    2026年4月6日

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  • Neil Hindman,
  • Dona Strauss

摘要

We investigate a notion of largeness introduced by Bergelson and Robertson. Given a notion R of largeness in a semigroup, a set is an almost R set if it differs from an R set by a set with Banach density zero. We investigate almost large sets for several notions of largeness, establishing the exact relationships among many of these sets for subsets of the set \(\mathbb {N}\) N of positive integers.