The combinatorial derivation

• Protasov, Igor V. ^[1]
  1. [1] Kyiv University
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 14, Nº. 2, 2013, págs. 171-178
• Idioma: inglés
• DOI: 10.4995/agt.2013.1587
• Enlaces
  • Texto completo
• Resumen

  • 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 $d$.

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