How do I prove that the function $f(x) = d(u,x)$ who maps the metric space $M$ into the real numbers are continuous? u is a fixed point of the metric space $M$.
Continuity of f where f(x) =d(u,x) maps the metric space M into the real numbers
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$\begingroup$
functions
metric-spaces
continuity
1 Answers
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Hint: $d(u,x) \leq d(u,y) + d(x,y)$ and $d(u,y) \leq d(u,x) + d(x,y)$ yields that $|d(u,x) - d(u,y)| \leq d(x,y)$. Conclude.