Can you guys help me prove: Given a continuous and differentiable function (or surface) f: R^2 -> R, such that f(x,y) = z ... contour lines can always be drawn... the function is NOT bijective.(adsbygoogle = window.adsbygoogle || []).push({});

I've been thinking of choosing any arbitrary point and showing that the curves that intersect to form that point (over y-axis and x-axis) always manage to have certain z-values that are equal.

How do I point this is in mathematical terms?

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# That given a continuous surface, contour lines exist

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