The combinatorial derivation

Igor V. Protasov

Abstract

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 $d$.

Keywords

Combinatorial derivation; $\Delta$-trajectories; large, small and thin subsets of groups; partitions of groups; Stone-\v{C}ech compactification of a group

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References

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1. Asymptotic structures of cardinals
Oleksandr Petrenko, Igor V. Protasov, Sergii Slobodianiuk
Applied General Topology  vol: 15  issue: 2  first page: 137  year: 2014  
doi: 10.4995/agt.2014.3109



Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt