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Math Help - Distance function: continuous?

  1. #1
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    Distance function: continuous?

    Let (X,d) be a metric space. Prove that the distance function
    d: X \times X \rightarrow \mathbb{R} is continuous, assuming that XxX has the product topology that results from each copy of X having the topology induced by d.
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  2. #2
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    Quote Originally Posted by Andreamet View Post
    Let (X,d) be a metric space. Prove that the distance function
    d: X \times X \rightarrow \mathbb{R} is continuous, assuming that XxX has the product topology that results from each copy of X having the topology induced by d.
    Remember, a function  f:R \rightarrow R is said to be continuous if, at the point  a \in R, if given  \epsilon > 0 , there is a  \delta > 0 such that

     |f(x) - f(a)| < \epsilon

    whenever:

     |x-a| < \delta
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