Partial Orders in Topological Spaces
If P is a partially ordered set that has also been given the structure of a topological space, then it is customary to assume that {(a, b) : a ≤ b} is a closed subset of the topological product space . Under this assumption partial order relations are well behaved at limits in the sense that if, and ai ≤ bi for all i, then a ≤ b.
Read more about this topic: Partially Ordered Set
Famous quotes containing the words partial, orders and/or spaces:
“It is characteristic of the epistemological tradition to present us with partial scenarios and then to demand whole or categorical answers as it were.”
—Avrum Stroll (b. 1921)
“One cannot be a good historian of the outward, visible world without giving some thought to the hidden, private life of ordinary people; and on the other hand one cannot be a good historian of this inner life without taking into account outward events where these are relevant. They are two orders of fact which reflect each other, which are always linked and which sometimes provoke each other.”
—Victor Hugo (1802–1885)
“Every true man is a cause, a country, and an age; requires infinite spaces and numbers and time fully to accomplish his design;—and posterity seem to follow his steps as a train of clients.”
—Ralph Waldo Emerson (1803–1882)