Let \(U\subseteq M\) be a an open subset of a manifold \(M\) a let \(V\subseteq\mathbb R^{n}\) be an open subset of the \(n\)-dimensional metric space or real numbers \(\mathbb {R} ^{n}\).
Every homeomorphism \(\varphi \colon U\longrightarrow V\) is called a (topological) chart of \(M\).