Compact Element
In the mathematical area of order theory, the compact or finite elements of a partially ordered set are those elements that cannot be subsumed by a supremum of any non-empty directed set that does not already contain members above the compact element.
Note that there are other notions of compactness in mathematics; also, the term "finite" in its normal set theoretic meaning does not coincide with the order-theoretic notion of a "finite element".
Read more about Compact Element: Formal Definition, Examples, Algebraic Posets, Applications, Literature
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