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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

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I've been reading about space filling curves, and been asking myself this question. If $f: \mathbb{R}^{2} \rightarrow \mathbb{R}$ is a continuous open map, is it true that $\forall x \in$ range$(f)$ …
John Bluto's user avatar