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    Metric space

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    Let X be a metric space and x0 in X. Define a function f: X --> R (all real numbers) by f(x) = d(x,x0). Show that f is continuous.
    HINT: Prove the variant of the triangle inequality which says
    |d(x,z)-d(y,z)|< d(x,y) for any x,y,z in X

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    Solution Summary

    This show show to prove a function in a metric space is continuous.