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I've found very nice problem in math analysis book but I can't solve it:

We define $c$ function as $c : \mathbb{I^2} \rightarrow \mathbb{R}$ and $\mathbb{I^2}$ means closed square in $\mathbb{R^2}$ with vertices $( \pm 1, \pm 1)$.

Is it true that continuous function $c$ can be injective?

How can I solve this problem?

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    Your question is not well-defined? Are you claiming that ***for all*** continuous functions $c$ from the unit square to the plane, $c$ is injective?2012-07-13
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    I asked whether that the function exists.2012-07-13

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