Prove that $f:X \rightarrow \mathbb{R}$ is constant.

Asked Jun 09 '19 at 06:45

Active Jun 09 '19 at 08:15

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Let $(X,d)$ be a connected metric space and $f:X \rightarrow \mathbb{R}$ be a continuous function. Suppose that for every $x \in X$ there exists an open set $U \subseteq X$ so that $x \in U$ and ${f|}_n:U \rightarrow \mathbb{R}$ is constant. Prove that $f:X \rightarrow \mathbb{R}$ is constant.

I don't know where to start with this problem

edited Jun 09 '19 at 08:15

Henno Brandsma

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asked Jun 09 '19 at 06:45

ana

See my answer here – Henno Brandsma Jun 09 '19 at 06:55

Prove that $f:X \rightarrow \mathbb{R}$ is constant.

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