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:
“What compact mean you to have with us?
Will you be pricked in number of our friends,
Or shall we on, and not depend on you?”
—William Shakespeare (1564–1616)
“We have a great deal more kindness than is ever spoken. Maugre all the selfishness that chills like east winds the world, the whole human family is bathed with an element of love like a fine ether.”
—Ralph Waldo Emerson (1803–1882)