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)
“Selflessness is like waiting in a hospital
In a badly-fitting suit on a cold wet morning.
Selfishness is like listening to good jazz
With drinks for further orders and a huge fire.”
—Philip Larkin (1922–1986)
“When I consider the short duration of my life, swallowed up in the eternity before and after, the little space which I fill and even can see, engulfed in the infinite immensity of spaces of which I am ignorant and which know me not, I am frightened and am astonished at being here rather than there. For there is no reason why here rather than there, why now rather than then.”
—Blaise Pascal (1623–1662)