منابع مشابه
Small Sets Satisfying the Central Sets Theorem
The Central Sets Theorem is a powerful theorem, one of whose consequences is that any central set in N contains solutions to any partition regular system of homogeneous linear equations. Since at least one set in any finite partition of N must be central, any of the consequences of the Central Sets Theorem must be valid for any partition of N. It is a result of Beiglböck, Bergelson, Downarowicz...
متن کاملA Multidimensional Central Sets Theorem
t∈α xt : α ∈ Pf (ω)}. A set A ⊆ N is called an IP-set iff there exists a sequence 〈xn〉n=0 in N such that FS(〈xn〉n=0) ⊆ A. (This definitions make perfect sense in any semigroup (S, ·) and we indeed plan to use them in this context. FS is an abbriviation of finite sums and will be replaced by FP if we use multiplicative notation for the semigroup operation.) Now Hindman’s Theorem states that in a...
متن کاملA Multidimensional Central Sets Theorem
t∈α xt : α ∈ Pf (ω)}. A set A ⊆ N is called an IP-set iff there exists a sequence 〈xn〉n=0 in N such that FS(〈xn〉n=0) ⊆ A. (This definitions make perfect sense in any semigroup (S, ·) and we indeed plan to use them in this context. FS is an abbriviation of finite sums and will be replaced by FP if we use multiplicative notation for the semigroup operation.) Now Hindman’s Theorem states that in a...
متن کاملDensity near zero
Let $S$ be a dense subsemigroup of $(0,+infty)$. In this paper, we state definition of thick near zero, and also we will introduce a definition that is equivalent to the definition of piecewise syndetic near zero which presented by Hindman and Leader in [6]. We define density near zero for subsets of $S$ by a collection of nonempty finite subsets of $S$ and we investigate the conditions un...
متن کاملA simple characterization of sets satisfying the Central Sets Theorem
Central subsets of a discrete semigroup S have very strong combinatorial properties which are a consequence of the Central Sets Theorem. Call a set a C-set if it satisfies the conclusion of the Central Sets Theorem. We obtain here a reasonably simple characterization of C-sets in an arbitrary discrete semigroup.
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2016
ISSN: 0166-8641
DOI: 10.1016/j.topol.2016.06.014