The combinatorial derivation

Authors

  • Igor V. Protasov Kyiv University

DOI:

https://doi.org/10.4995/agt.2013.1587

Keywords:

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

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 $d$.

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References

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Published

2013-09-18

How to Cite

[1]
I. V. Protasov, “The combinatorial derivation”, Appl. Gen. Topol., vol. 14, no. 2, pp. 171–178, Sep. 2013.

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