On representation of semigroups of inclusion hyperspaces
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 semigr...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Vasyl Stefanyk Precarpathian National University
2013-01-01
|
| Series: | Karpatsʹkì Matematičnì Publìkacìï |
| Online Access: | http://journals.pu.if.ua/index.php/cmp/article/view/36 |
| _version_ | 1818879160092721152 |
|---|---|
| author | V. M. Gavrylkiv |
| author_facet | V. M. Gavrylkiv |
| author_sort | V. M. Gavrylkiv |
| collection | DOAJ |
| description | 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 $X$. |
| first_indexed | 2024-12-19T14:25:39Z |
| format | Article |
| id | doaj.art-9ffa8308085949888467693191e159a5 |
| institution | Directory Open Access Journal |
| issn | 2075-9827 2313-0210 |
| language | English |
| last_indexed | 2024-12-19T14:25:39Z |
| publishDate | 2013-01-01 |
| publisher | Vasyl Stefanyk Precarpathian National University |
| record_format | Article |
| series | Karpatsʹkì Matematičnì Publìkacìï |
| spelling | doaj.art-9ffa8308085949888467693191e159a52022-12-21T20:17:37ZengVasyl Stefanyk Precarpathian National UniversityKarpatsʹkì Matematičnì Publìkacìï2075-98272313-02102013-01-0121243410.15330/cmp.2.1.24-3436On representation of semigroups of inclusion hyperspacesV. M. Gavrylkiv0Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, UkraineGiven 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 $X$.http://journals.pu.if.ua/index.php/cmp/article/view/36 |
| spellingShingle | V. M. Gavrylkiv On representation of semigroups of inclusion hyperspaces Karpatsʹkì Matematičnì Publìkacìï |
| title | On representation of semigroups of inclusion hyperspaces |
| title_full | On representation of semigroups of inclusion hyperspaces |
| title_fullStr | On representation of semigroups of inclusion hyperspaces |
| title_full_unstemmed | On representation of semigroups of inclusion hyperspaces |
| title_short | On representation of semigroups of inclusion hyperspaces |
| title_sort | on representation of semigroups of inclusion hyperspaces |
| url | http://journals.pu.if.ua/index.php/cmp/article/view/36 |
| work_keys_str_mv | AT vmgavrylkiv onrepresentationofsemigroupsofinclusionhyperspaces |