locally Euclidean

Definition

Let $X$ be a topological space, then $X$ is called locally Euclidean of dimension $n$ if for every $x \in X$ there exists a neighborhood $U \subseteq X$, a $V \subseteq \mathbb{R}^n$, and a homeomorphism $\phi: U \to V$.

Then, the triple $(\varphi,U,V)$ is called a chart (around $p$).

References

1. http://staff.ustc.edu.cn/~wangzuoq/Courses/18F-Manifolds/Notes/Lec01.pdf
2. https://planetmath.org/locallyeuclidean