Retracts of Posets: the Chain-gap Property and the Selection Property Are Independent
نویسندگان
چکیده
Posets which are retract of products of chains are characterized by means of two properties: the chain-gap property and the selection property (Rival and Wille, 1981 [8]). Examples of posets with the selection property and not the chain-gap property are easy to find. To date, the Boolean lattice P(ω1)/F in was the sole example of lattice without the selection property [8]. 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 [8].
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