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Suppose $a$ is a point of the metric space $S$. Define $g(p) = d(a,p)$ with $p \in S$. Prove $g$ is uniformly continuous.

Also, if possible, don't use Lipschitz continuity or denseness. We haven't covered those in class so I'll have no idea what you're talking about.

  • 3
    $|g(p)-g(q)|\leqslant d(p,q)$.2011-12-13
  • 1
    $g(p)+d(p,q)\geq g(q)$ by the triangle inequality2011-12-13

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