poset

Noun

Meaning

poset (plural posets)

(set theory, order theory) A partially ordered set.

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Examples

Any geometric polyhedron is then said to be a "realization" in real space of the abstract poset. Source: Internet

An abstract polyhedron is a certain kind of partially ordered set (poset) of elements, such that adjacencies, or connections, between elements of the set correspond to adjacencies between elements (faces, edges, etc.) of a polyhedron. Source: Internet

A poset consists of a set together with a binary relation that indicates that, for certain pairs of elements in the set, one of the elements precedes the other. Source: Internet

Definition A partially ordered set (poset) P is said to satisfy the ascending chain condition (ACC) if every strictly ascending sequence of elements eventually terminates. Source: Internet

For this process, elements of the poset are mapped to (Dedekind-) cuts, which can then be mapped to the underlying posets of arbitrary complete lattices in much the same way as done for sets and free complete (semi-) lattices above. Source: Internet

Any such poset has a dual poset. Source: Internet

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