Locally Euclidean

Definition

Consider a Topological Space $(M,\mathcal{T})$. $\forall p\in M,\exists {\mathcal{N}}_x\subset M,\exists \varphi :{\mathcal{N}}_x\to \varphi ({\mathcal{N}}_x)\subset {\mathbb{R}}^n$ where ${\mathcal{N}}_x$ is the Neighborhood of $x$, and $\varphi$ is Homeomorphism and is called a coordinate chart.