Topology Induced By The Order
If F is equipped with the order topology arising from the total order ≤, then the axioms guarantee that the operations + and * are continuous, so that F is a topological field.
Read more about this topic: Ordered Field
Famous quotes containing the words induced and/or order:
“It is a misfortune that necessity has induced men to accord greater license to this formidable engine, in order to obtain liberty, than can be borne with less important objects in view; for the press, like fire, is an excellent servant, but a terrible master.”
—James Fenimore Cooper (1789–1851)
“I had to kick their law into their teeth in order to save them.
However I have heard that sometimes you have to deal
Devilishly with drowning men in order to swim them to shore.
Or they will haul themselves and you to the trash and the fish beneath.”
—Gwendolyn Brooks (b. 1917)