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Miklos Schweitzer 1972_2

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November 5, 2008
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Problem Statement

Let ≤ \leq be a reflexive, antisymmetric relation on a finite set A A. Show that this relation can be extended to an appropriate finite superset B B of A A such that ≤ \leq on B B remains reflexive, antisymmetric, and any two elements of B B have a least upper bound as well as a greatest lower bound. (The relation ≤ \leq is extended to B B if for x,y∈A,x≤y x,y \in A , x \leq y holds in A A if and only if it holds in B B.) E. Freid
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