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It is a general thought so I hope it make any sense, it the case of a function $f:\mathbb{R}\rightarrow \mathbb{R}$ we could talk about onto and isomorphic map. is it the same with $g:\mathbb{R^2}\rightarrow \mathbb{R}$ or $h:\mathbb{R^3}\rightarrow \mathbb{R^2}$

do not we "lose" data going from an higher dimension to a smaller one?

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    Such a map can be onto ("surjective"), but it cannot be one-to-one ("injective") or isomorphic ("bijective"). – 2017-01-15

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