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Continuity

  • Definition: Let (S, d) and (T, p) be metric spaces and let f: S -> T be a function from S to T. The function f is said to be continuous at a point y in S if for every epsilon > 0 there is a delta > 0 such that p(f(x), f(y)) < epsilon whenever d(x, y) < delta. If f is continuous at every point of a subset of A of S, we say f is continuous on A.

    Source: Mathematical Analysis, second edition by Tom M. Apostol

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