Is there a continuous surjective map between $ mathbb R ^ 2 to S ^ 1 $?

I had found such a map with domain $ mathbb R ^ 2 / ${$ 0 $}.

But I can not find if we insert 0 there?

Every help is appreciated

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# Is there a continuous surjective map between $ mathbb R ^ 2 and S ^ 1 $

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Is there a continuous surjective map between $ mathbb R ^ 2 to S ^ 1 $?

I had found such a map with domain $ mathbb R ^ 2 / ${$ 0 $}.

But I can not find if we insert 0 there?

Every help is appreciated

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