The combinatorial derivation
Let $G$ be a group, $\mathcal{P}_G$ be the family of all subsets of $G$. For a subset $A\subseteq G$, we put $\Delta(A)=\{g\in G:|gA\cap A|=\infty\}$. The mapping $\Delta:\mathcal{P}_G\rightarrow\mathcal{P}_G$, $A\mapsto\Delta(A)$, is called a combinatorial derivation and can be considered as an ana...
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| Format: | Article |
| Language: | English |
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Universitat Politècnica de València
2013-09-01
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| Series: | Applied General Topology |
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| Online Access: | http://polipapers.upv.es/index.php/AGT/article/view/1587 |
| _version_ | 1818202351346909184 |
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| author | Igor V. Protasov |
| author_facet | Igor V. Protasov |
| author_sort | Igor V. Protasov |
| collection | DOAJ |
| description | Let $G$ be a group, $\mathcal{P}_G$ be the family of all subsets of $G$. For a subset $A\subseteq G$, we put
$\Delta(A)=\{g\in G:|gA\cap A|=\infty\}$. The mapping $\Delta:\mathcal{P}_G\rightarrow\mathcal{P}_G$, $A\mapsto\Delta(A)$, is called a combinatorial derivation and can be considered as an analogue of the topological derivation $d:\mathcal{P}_X\rightarrow\mathcal{P}_X$, $A\mapsto A^d$, where $X$ is a topological space and $A^d$ is the set of all limit points of $A$. Content: elementary properties, thin and almost thin subsets, partitions, inverse construction and $\Delta$-trajectories, $\Delta$ and $d$. |
| first_indexed | 2024-12-12T03:08:04Z |
| format | Article |
| id | doaj.art-0688cae4196a4204923a5d7fd6bc91ba |
| institution | Directory Open Access Journal |
| issn | 1576-9402 1989-4147 |
| language | English |
| last_indexed | 2024-12-12T03:08:04Z |
| publishDate | 2013-09-01 |
| publisher | Universitat Politècnica de València |
| record_format | Article |
| series | Applied General Topology |
| spelling | doaj.art-0688cae4196a4204923a5d7fd6bc91ba2022-12-22T00:40:28ZengUniversitat Politècnica de ValènciaApplied General Topology1576-94021989-41472013-09-0114217117810.4995/agt.2013.15871371The combinatorial derivationIgor V. Protasov0Kyiv UniversityLet $G$ be a group, $\mathcal{P}_G$ be the family of all subsets of $G$. For a subset $A\subseteq G$, we put $\Delta(A)=\{g\in G:|gA\cap A|=\infty\}$. The mapping $\Delta:\mathcal{P}_G\rightarrow\mathcal{P}_G$, $A\mapsto\Delta(A)$, is called a combinatorial derivation and can be considered as an analogue of the topological derivation $d:\mathcal{P}_X\rightarrow\mathcal{P}_X$, $A\mapsto A^d$, where $X$ is a topological space and $A^d$ is the set of all limit points of $A$. Content: elementary properties, thin and almost thin subsets, partitions, inverse construction and $\Delta$-trajectories, $\Delta$ and $d$.http://polipapers.upv.es/index.php/AGT/article/view/1587Combinatorial derivation$\Delta$-trajectorieslarge, small and thin subsets of groupspartitions of groupsStone-\v{C}ech compactification of a group |
| spellingShingle | Igor V. Protasov The combinatorial derivation Applied General Topology Combinatorial derivation $\Delta$-trajectories large, small and thin subsets of groups partitions of groups Stone-\v{C}ech compactification of a group |
| title | The combinatorial derivation |
| title_full | The combinatorial derivation |
| title_fullStr | The combinatorial derivation |
| title_full_unstemmed | The combinatorial derivation |
| title_short | The combinatorial derivation |
| title_sort | combinatorial derivation |
| topic | Combinatorial derivation $\Delta$-trajectories large, small and thin subsets of groups partitions of groups Stone-\v{C}ech compactification of a group |
| url | http://polipapers.upv.es/index.php/AGT/article/view/1587 |
| work_keys_str_mv | AT igorvprotasov thecombinatorialderivation AT igorvprotasov combinatorialderivation |