Basic Definitions
LU(A) is the set of all lower bounds of the set of all upper bounds of the subset A of a partially ordered set.
A subset I of a partially ordered set (P, ≤) is a Frink ideal, if the following condition holds:
For every finite subset S of P, S I implies that LU(S) I.
A subset I of a partially ordered set (P,≤) is a normal ideal or a cut if LU(I) I.
Read more about this topic: Frink Ideal
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