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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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level sets portrait near a critical point

Let $f:\mathbb{R}^{2}\rightarrow\mathbb{R}$ be a smooth ($C^{\infty}$) function and $O$ be an isolated critical point of $f$. I am looking at the local level sets diagram near $O$ from topological poi …
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