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
Famous quotes containing the words compact and/or element:
“The Puritans, to keep the remembrance of their unity one with another, and of their peaceful compact with the Indians, named their forest settlement CONCORD.”
—Ralph Waldo Emerson (1803–1882)
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—William Booth (1829–1912)