History
The first published definition of uniform continuity was by Heine in 1870, and in 1872 he published a proof that a continuous function on an open interval need not be uniformly continuous. The proofs are almost verbatim given by Dirichlet in his lectures on definite integrals in 1854. The definition of uniform continuity appears earlier in the work of Bolzano where he also proved that continuous functions on an open interval do not need to be uniformly continuous. In addition he also states that a continuous function on a closed interval is uniformly continuous, but he does not give a complete proof.
Read more about this topic: Uniform Continuity
Famous quotes containing the word history:
“Social history might be defined negatively as the history of a people with the politics left out.”
—G.M. (George Macaulay)
“In front of these sinister facts, the first lesson of history is the good of evil. Good is a good doctor, but Bad is sometimes a better.”
—Ralph Waldo Emerson (1803–1882)
“Don’t give your opinions about Art and the Purpose of Life. They are of little interest and, anyway, you can’t express them. Don’t analyse yourself. Give the relevant facts and let your readers make their own judgments. Stick to your story. It is not the most important subject in history but it is one about which you are uniquely qualified to speak.”
—Evelyn Waugh (1903–1966)