Retracts of Posets: The Chain_gap Property and the Selection Property are Independant

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dc.creatorDuffus, Dwight
dc.creatorLaflamme, Claude
dc.creatorPouzet, Maurice
dc.date2006-12-15
dc.date.accessioned2026-07-07T07:35:40Z
dc.date.available2026-07-07T07:35:40Z
dc.descriptionPosets which are retract of products of chains are characterized by means of two properties: \emph{the chain-gap property} and \emph{the selection property} (Rival and Wille, 1981 \cite {R-W}). Examples of posets with the selection property and not the chain-gap property are easy to find. To date, the Boolean lattice $\Power (ω_1)/Fin$ was the sole example of lattice without the selection property \cite {R-W}. We prove that it does not have the chain-gap property. We provide an example of a lattice which has the chain-gap property but not the selection property. This answer questions raised in \cite {R-W}.
dc.description10 pages
dc.identifierhttps://arxiv.org/abs/math/0612458
dc.identifierhttp://arxiv.org/abs/math/0612458
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/120169
dc.subjectCombinatorics
dc.subject06A, 06B
dc.titleRetracts of Posets: The Chain_gap Property and the Selection Property are Independant
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