Partial semigroup partial dynamical systems and Partial Central Sets
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910476425756672 |
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| author | Goodarzi, H. Tootkaboni, M. A. Ghosh, Arpita |
| author_facet | Goodarzi, H. Tootkaboni, M. A. Ghosh, Arpita |
| contents | H. Furstenberg defined Central sets in $\mathbb{N}$ by using the notions of topological dynamics, later Bergelson and Hindman characterized central sets in $\mathbb{N}$ and also in arbitrary semigroup in terms of algebra of Stone-Čech compactification of that set. We state the new notion of large sets in a partial semigroup setting and characterize the algebraic structure of the sets by using the algebra of Stone-Čech compactification. By using these notions, we introduce the \emph{Partial Semigroup Partial Dynamical System(PSPDS)} and show that topological dynamical characterization of central sets in a partial semigroup is equivalent to the usual algebraic characterization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_04672 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Partial semigroup partial dynamical systems and Partial Central Sets Goodarzi, H. Tootkaboni, M. A. Ghosh, Arpita Combinatorics Dynamical Systems 2020 MSC: 37B02, 22A15 Secondary: 05D10. 37B02, 22A15, 05D10 H. Furstenberg defined Central sets in $\mathbb{N}$ by using the notions of topological dynamics, later Bergelson and Hindman characterized central sets in $\mathbb{N}$ and also in arbitrary semigroup in terms of algebra of Stone-Čech compactification of that set. We state the new notion of large sets in a partial semigroup setting and characterize the algebraic structure of the sets by using the algebra of Stone-Čech compactification. By using these notions, we introduce the \emph{Partial Semigroup Partial Dynamical System(PSPDS)} and show that topological dynamical characterization of central sets in a partial semigroup is equivalent to the usual algebraic characterization. |
| title | Partial semigroup partial dynamical systems and Partial Central Sets |
| topic | Combinatorics Dynamical Systems 2020 MSC: 37B02, 22A15 Secondary: 05D10. 37B02, 22A15, 05D10 |
| url | https://arxiv.org/abs/2406.04672 |