Definition
Let X and Y be metric spaces, and let f be a function from X to Y. Then f is Cauchy-continuous if and only if, given any Cauchy sequence (x1, x2, …) in X, the sequence (f(x1), f(x2), …) is a Cauchy sequence in Y.
Read more about this topic: Cauchy-continuous Function
Famous quotes containing the word definition:
“I’m beginning to think that the proper definition of “Man” is “an animal that writes letters.””
—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)
“It’s a rare parent who can see his or her child clearly and objectively. At a school board meeting I attended . . . the only definition of a gifted child on which everyone in the audience could agree was “mine.””
—Jane Adams (20th century)
“The man who knows governments most completely is he who troubles himself least about a definition which shall give their essence. Enjoying an intimate acquaintance with all their particularities in turn, he would naturally regard an abstract conception in which these were unified as a thing more misleading than enlightening.”
—William James (1842–1910)