MAT237Y1 : mat237 1-8.pdf

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A function fff : s rn is said to be uniformly continuous on the set s whenever. Such that xxx, yyy s |xxx yyy| < = |fff (xxx fff (yyy)| < . Aaa s such that xxx s |xxx aaa| < = |fff (xxx fff (aaa)| < . |fff (xxx) fff (yyy)| will be bounded (that is, under control) on a set s. see exercise 1, holder continuity. Uniform continuity is continuity without the complications discussed in the proof of theorem 1. 10. The proof uses uniform continuity to prove > 0 such that.

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