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Any POSET can be represented as an access graph G = (V, E), in which vertices represents groups and edges represent connectivity from the predecessor to successor.
If I and J are down-sets of the poset P, then there is an x [member of] P whose addition to or removal from I decreases the distance to J.
Then there exists an isomorphism [psi]: Nuc(A)[right arrow]Con(A) of posets.
2 The Height Function on a Well-Founded Poset, the Height of an age and its Relation with the Profile
The poset P is contained in DM(P) by the embedding x [?
An (upper) closure operator, or simply a closure, on a poset P is an operator [Rho]: P [right arrow] P monotone, idempotent and extensive (i.
For every quadrangulation Q, there should be as many elements in the poset attached to Q as there are serpent nests in Q.
This idea is plausible because the double power locale monad is double exponentiation relative to any topos [epsilon], but a direct application of the result offered here is not possible because 1 is not generating in the category of posets relative to an arbitrary topos [epsilon].
The former class is associated to finite posets, while the latter corresponds to dedekind complete finite posets.
A subset A of a poset (S, [less than or equal to]) is said to be a down-set if s [member of] A whenever s [less than or equal to] a for s [member of] S, a [member of] A.
gt; be a poset with a bottom element [perpendicular to] (i.
This technique takes into account idiosyncrasies of the topology of the poset being encoded that are quite likely to occur in practice.