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:
“If man is reduced to being nothing but a character in history, he has no other choice but to subside into the sound and fury of a completely irrational history or to endow history with the form of human reason.”
—Albert Camus (1913–1960)
“There is no history of how bad became better.”
—Henry David Thoreau (1817–1862)
“The history of progress is written in the blood of men and women who have dared to espouse an unpopular cause, as, for instance, the black man’s right to his body, or woman’s right to her soul.”
—Emma Goldman (1869–1940)