Let $z$ be a point in a metric space $(X, p)$. Why is $f: X\to\mathbb{R}$, $f(x)=p(x,z)$ uniformly continuous?
I could draw a picture that illustrates the idea, please help me with the proof.
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The triangle inequality. – Aug 31 '16 at 01:19
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@ArcticChar this is different. That post is a proof of continuity. Here i am asking about uniform continuity – user1559897 Aug 31 '16 at 01:28
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1@user1559897 And if you read the top answer, it explains explicitly how to prove uniform continuity. (And the question also asked for uniform continuity.) – Aug 31 '16 at 01:29
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@T.Bongers It wasnt, the uniform continuity in the question was added by me. – Aug 31 '16 at 01:31
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My mistake, sorry. – Aug 31 '16 at 01:32