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Article Dans Une Revue Algebra Universalis Année : 2008

Retracts of posets: the chain-gap property and the selection property are independent

Dwight Duffus
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Claude Laflamme
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Maurice Pouzet
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Résumé

Posets which are retracts of products of chains are characterized by means of two properties: \emph{the chain-gap property} and \emph{ the selection property} (Rival and Wille \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 $\Power (\omega_1)/Fin$ has been the sole example of a lattice without the selection property \cite {R-W}. We prove that it also fails to have the chain-gap property. In addition, we provide an example of a lattice which has the chain-gap property but not the selection property. This answers questions raised in \cite {R-W}

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Dates et versions

hal-00863477 , version 1 (18-09-2013)

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  • HAL Id : hal-00863477 , version 1

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Dwight Duffus, Claude Laflamme, Maurice Pouzet. Retracts of posets: the chain-gap property and the selection property are independent. Algebra Universalis, 2008, 59 (1-2), pp.243-255. ⟨hal-00863477⟩
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