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Let (M,d) be a metric space. $A \subseteq M$ and closed. Further let $U \subseteq M$ a open subset and $A \subseteq U$.

Does a continouos function $f: M \rightarrow [0,1]$ exist such that $f(x)=1$ if $x \in A$ and $f(x)=0$ if $x \notin U$

I dont't know how to approach this. Would be thankful for hints

John.W
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    This appears to be https://en.wikipedia.org/wiki/Urysohn%27s_lemma in the case of metric spaces (where the closed sets in question are $A$ and $M \setminus U$). – Ian Sep 25 '21 at 18:43
  • @Ian thank you! – John.W Sep 25 '21 at 18:46

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