locally finite poset
Every locally finite poset is also chain finite, but the converse does not hold. To see this, define a partial order on by the rule that if and only if or . Thus is the minimum element, is the maximum element, and the remaining elements form an infinite antichain. Every bounded chain in this poset is finite but the entire poset is an infinite interval, so the poset is chain finite but not locally finite.
|Title||locally finite poset|
|Date of creation||2013-03-22 14:09:15|
|Last modified on||2013-03-22 14:09:15|
|Last modified by||mps (409)|