Dynamical characterizations of combinatorially rich sets near zero
| Autor: | Sourav Kanti Patra |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Discrete mathematics
Algebraic structure 010102 general mathematics Mathematics::General Topology Dynamical Systems (math.DS) 01 natural sciences 010101 applied mathematics FOS: Mathematics Mathematics - Combinatorics Combinatorics (math.CO) Geometry and Topology Compactification (mathematics) Mathematics - Dynamical Systems 0101 mathematics Mathematics |
| Zdroj: | Topology and its Applications. 240:173-182 |
| ISSN: | 0166-8641 |
| Popis: | Hindman and Leader first introduced the notion of Central sets near zero for dense subsemigroups of $((0,\infty),+)$ and proved a powerful combinatorial theorem about such sets. Using the algebraic structure of the Stone-$\breve{C}$ech compactification, Bayatmanesh and Tootkabani generalized and extended this combinatorial theorem to the central theorem near zero. Algebraically one can define quasi-central set near zero for dense subsemigroup of $((0,\infty),+)$, and they also satisfy the conclusion of central sets theorem near zero. In a dense subsemigroup of $((0,\infty),+)$, C-sets near zero are the sets, which satisfies the conclusions of the central sets theorem near zero. Like discrete case, we shall produce dynamical characterizations of these combinatorically rich sets near zero. Comment: 12 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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