I am supposed to give a counterexample showing the conclusion is false when $A$ is not closed. I tried to find one when $M$ is Euclidean space but kept failing... Could anyone please show me a counterexample?
2026-02-22 17:57:08.1771783028
Giving a counterexample for the extension lemma of smooth functions
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Consider $f(x)=1/x$ defined on $\mathbb{R}-\{0\}$, you cannot extend it at $0$