<s>[INST] By definition, \(\Gamma\) is a _topological manifold_ of dimension \(n\) if for any point \(x \in \Gamma\) there exists a neighborhood \(U \subset \Gamma\) of (\(x\)) and a homeomorphism \(\varphi : U \rightarrow \mathbb{R}_n\), where \(\mathbb{R}n\) is the \(n\) -dimensional space with the standard topology.[/INST]