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# The dynamical look at the subsets of a group

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 dc.contributor.author Protasov, Igor V. es_ES dc.contributor.author Slobodianiuk, Serhii es_ES dc.date.accessioned 2016-10-21T07:07:35Z dc.date.available 2016-10-21T07:07:35Z dc.date.issued 2016-10-01 dc.identifier.issn 1576-9402 dc.identifier.uri http://hdl.handle.net/10251/72544 dc.description.abstract [EN] We consider the action of a group $G$ on the family $\mathcal{P}(G)$ of all subsets of $G$ by the right shifts $A\mapsto Ag$ and give the dynamical characterizations of thin, $n$-thin, sparse and scattered subsets.For $n\in\mathbb{N}$, a subset $A$ of a group $G$ is called $n$-thin if $g_0A\cap\dots\cap g_nA$ is finite for all distinct $g_0,\dots,g_n\in G$.Each $n$-thin subset of a group of cardinality $\aleph_0$ can be partitioned into $n$ $1$-thin subsets but there is a $2$-thin subset in some Abelian group of cardinality $\aleph_2$ which cannot be partitioned into two $1$-thin subsets. We eliminate the gap between $\aleph_0$ and $\aleph_2$ proving that each $n$-thin subset of an Abelian group of cardinality $\aleph_1$ can be partitioned into $n$ $1$-thin subsets. es_ES dc.language Inglés es_ES dc.publisher Universitat Politècnica de València dc.relation.ispartof Applied General Topology dc.rights Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) es_ES dc.subject Thin es_ES dc.subject Sparse and scatterad subsets of a group es_ES dc.subject Recurrent point es_ES dc.subject Chromatic number of a graph es_ES dc.title The dynamical look at the subsets of a group es_ES dc.type Artículo es_ES dc.date.updated 2016-10-20T12:27:47Z dc.identifier.doi 10.4995/agt.2015.3584 dc.rights.accessRights Abierto es_ES dc.description.bibliographicCitation Protasov, IV.; Slobodianiuk, S. (2016). The dynamical look at the subsets of a group. Applied General Topology. 16(2):217-224. doi:10.4995/agt.2015.3584 es_ES dc.description.accrualMethod SWORD es_ES dc.relation.publisherversion https://doi.org/10.4995/agt.2015.3584 es_ES dc.description.upvformatpinicio 217 es_ES dc.description.upvformatpfin 224 es_ES dc.type.version info:eu-repo/semantics/publishedVersion es_ES dc.description.volume 16 dc.description.issue 2 dc.identifier.eissn 1989-4147
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