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
Famous quotes containing the words basic and/or definitions:
“Just as the constant increase of entropy is the basic law of the universe, so it is the basic law of life to be ever more highly structured and to struggle against entropy.”
—Václav Havel (b. 1936)
“What I do not like about our definitions of genius is that there is in them nothing of the day of judgment, nothing of resounding through eternity and nothing of the footsteps of the Almighty.”
—G.C. (Georg Christoph)