On representation of semigroups of inclusion hyperspaces
| Autor: | V. M. Gavrylkiv |
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| Jazyk: | angličtina |
| Rok vydání: | 2010 |
| Předmět: | |
| Zdroj: | Karpatsʹkì Matematičnì Publìkacìï, Vol 2, Iss 1, Pp 24-34 (2010) Karpatsʹkì Matematičnì Publìkacìï, Vol 2, Iss 1, Pp 24-34 (2013) |
| ISSN: | 2075-9827 |
| Popis: | Given a group $X$ we study the algebraic structure of the compact right-topological semigroup $G(X)$ consisting of inclusion hyperspaces on $X$. This semigroup contains the semigroup $\lambda(X)$ of maximal linked systems as a closed subsemigroup. We construct a faithful representation of the semigroups $G(X)$ and $\lambda(X)$ in the semigroup $\mathbf P(X)^{\mathbf P(X)}$ of all self-maps of the power-set $\mathbf P(X)$. Using this representation we prove that each minimal left ideal of $\lambda(X)$ is topologically isomorphic to a minimal left ideal of the semigroup $\mathbf{pT}^{\mathbf{pT}}$, where by $\mathbf{pT}$ we denote the family of pretwin subsets of $X$. |
| Databáze: | OpenAIRE |
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