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)
“The newspapers, especially those in the East, are amazingly superficial and ... a large number of news gatherers are either cynics at heart or are following the orders and the policies of the owners of their papers.”
—Franklin D. Roosevelt (1882–1945)
“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)