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Topology

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Continuous Extension

TOPO-WKCLG1

Let $f$ be a function defined on $\mathbb{Q} \cap [0,1]$ and suppose that $|f(x)-f(y)|<|x-y|$ for all $x,y \in \mathbb{Q} \cap [0,1]$.

When can $f$ be extended to a unique continuous function $\hat{f}$ on $[0,1]$?

A

Never

B

Sometimes

C

Always