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I know $f \colon \mathbb R^2 \to \mathbb R$ mean that f maps each ordered pair (which contains two numbers as input) to a single number (as output). What about the $f\colon \mathbb R^2 \times \mathbb R \to \mathbb R^2 \times \mathbb R^2$?

cmk
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Đặng Huy Hoàng
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    I know that the notation $f:\mathbb{R}^{n}\times \mathbb{R}^{m}\to \mathbb{R}^{k}\times \mathbb{R}^{l}$ is generally used in the context of implicit theorem and inverse function theorem. Maybe you can check that references. –  Nov 06 '20 at 03:31
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    The function takes a pair of real numbers and a real number and maps it to a pair of pairs of real numbers. This is equivalent to a map from $\mathbb R^3$ to $\mathbb R^4$ but there could be some context where it is natural to think of the domain and codomain this way. – John Douma Nov 06 '20 at 03:56

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