# Is there a continuous surjective from $S^1$ to $[0,1]$?

Is there a continuous surjective map from $S^1$ to $[0,1]$?

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What have you tried? –  Chris Eagle Oct 12 '12 at 8:09
More concretely, $f : S^1 = \{ e^{it} | 0 \le t < 2\pi \} \rightarrow [0,1]$ is given by $f(e^{it}) = |sin(t)|$ –  Hee Kwon Lee Oct 12 '12 at 8:17