Dedekind cut

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Dedekind cut

(German ˈdedəˌkɪnt)
n
1. (Mathematics) a method of according the same status to irrational and rational numbers, devised by Julius Wilhelm Dedekind (1831-1916)
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The former class is associated to finite posets, while the latter corresponds to dedekind complete finite posets.
It is well known (taking into account that dedekind graphs correspond to dedekind complete finite posets) that, in this case, D is dedekind.
The next paragraph of this section deals with some facts about Dedekind complete and universally complete vector lattices.
We mention that E is an AM-space with a unit which is not Dedekind complete (see Theorem 14 and Corollary 15).
satisfying (1), (2), (3) and (4) is continuous (or Dedekind complete) iff