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Chapter 3 The Space of Continuous Functions

space of continuous functions de ned on a metric space. Let C(X) denote the vector space of all continuous functions de ned on Xwhere (X;d) is a metric space. Recall that in the exercise we showed that there are many continuous functions in X. In general, in a metric space such as the real line, a continuous function may not be bounded.

  Exercise, Continuous, All continuous