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manifolds

\(\def\Real{\mathbb{R}}
\def\Comp{\mathbb{C}}
\def\Rat{\mathbb{Q}}
\def\Field{\mathbb{F}}
\def\Fun{\mathbf{Fun}}
\def\e{\mathbf{e}}
\def\f{\mathbf{f}}
\def\torus{\mathbb{T}}
\)

Manifolds are topological spaces that locally look like Euclidean spaces.

Formalism: charts and atlases. Beware of pathologies (long line; double point…)! Smooth manifolds vs. topological ones.

Inverse function theorem (for a …

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