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Intermediate Value Theorem

  • Definition: Let f: X -> Y be a continuous map, where X is a connected space and Y is an ordered set in the order topology. If a and b are two points of X and if r is a point of Y lying between f(a) and f(b), then there exists a point c of X such that f(c) = r.

    Source: Topology (second edition) by James R. Munkres

  • Example: f can be a real-valued function.

  • Listed under: Field Of Topology, Mathematical Analysis

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