Almost disjoint large subsets of semigroups

Carlson, Timothy J.; Hindman, Neil; McLeod, Jillian; Strauss, Dona

doi:10.1016/j.topol.2005.05.012

Cited by 10 publications

(7 citation statements)

References 6 publications

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“…The fact that U S is a left ideal in S * is stated in [78,Exercise 6.4.1]. That U S is also a right ideal in S * was first proved in [75]; there is a simpler proof in [15,Lemma 3.1], and we essentially repeat this proof below in a slightly more general context. We again write uv for u 2 v.…”

Section: P -Pointsmentioning

confidence: 87%

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Banach algebras on semigroups and on their compactifications

Dales¹,

Lau²,

Strauss³

2010

Memoirs of the AMS

121

164

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Chapter 1. Introduction Chapter 2. Banach algebras and their second duals Chapter 3. Semigroups Chapter 4. Semigroup algebras Chapter 5. Stone-Čech compactifications Chapter 6. The semigroup (βS, 2) Chapter 7. Second duals of semigroup algebras Chapter 8. Related spaces and compactifications Chapter 9. Amenability for semigroups Chapter 10. Amenability of semigroup algebras Chapter 11. Amenability and weak amenability for certain Banach algebras Chapter 12. Topological centres Chapter 13. Open problems

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Section: P -Pointsmentioning

confidence: 87%

“…For set K = K(βS), and take µ ∈ M (βS). It follows from [15,Theorem 2.3(i)] that there is a family {U α :…”

Section: L(g)| = 2 2 |G|mentioning

confidence: 99%

Banach algebras on semigroups and on their compactifications

Dales¹,

Lau²,

Strauss³

2010

Memoirs of the AMS

121

164

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“…Then we pick n such that Y ⊆ H n , so H n Y is ω-thick, and choose x ∈ X such that H n+1 x ⊆ H n X . If x ∈ i n F i x i , by (1), H n+1 ⊆ H n i n F i x i , contradicting (2). Thus, x ∈ F m x m for some m > n, by (1), H n+1 x ⊆ K m x m , contradicting (3).…”

Section: Theorem 43 For Every Infinite Group G Of Regular Cardinalimentioning

confidence: 89%

“…This statement was proved in [10] to show that every infinite totally bounded topological group can be partitioned in |G| dense subset. For generalization of this statement see [2,14]. We note that all above types of subsets are not of the specific group nature, but can be defined (see [12,13] or Section 2 below) for some general structures, namely the balleans, which are the counterparts of the uniform topological spaces.…”

Section: Introductionmentioning

confidence: 99%

Small subsets of groups

Протасов

2009

Topology and its Applications

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MSC: 54E15 22A15 20F69 03E05Keywords:κ-large subset κ-small subset κ-thin subset Stone-Čech compactification of a discrete group Ballean Ideal Given an infinite group G and an infinite cardinal κ |G|, we say that a. The subject of the paper is the family S κ of all κ-small subsets. We describe the left ideal of the right topological semigroup βG determined by S κ . We study interrelations between κ-small and other (P κ -small and κ-thin) subsets of groups, and prove that G can be generated by some 2-thin subsets. We partition G in countable many subsets which are κ-small for each κ ω. We show that [G] <κ is dual to S κ provided that either κ is regular and κ = |G|, or G is Abelian and κ is a limit cardinal, or G is a divisible Abelian group.

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“…In the dynamical terminology [17], left large and left prethick subsets are known under the names syndetic and piecewise syndetic. The adjectives small, thick and thin in our context appeared in [9], [10], [11] respectively. The sparse subsets were introduced in [15] and studied in [19].…”

Section: Diversity Of Subsetsmentioning

confidence: 99%