Locally Euclidean

Statements

Definition. (@GodNat14 pp. 8, @Boo75 pp. 6) A topological space $(X,\tau )$ is said to be locally Euclidean of dimension $n$ if there exists $n\in \mathbb{N}$ such that, for every $x\in X$, there exists a neighborhood $N(x)$ that is homeomorphic to a open ball of ${\mathbb{R}}^n$ having dimension $n$. Such a homeomorphism is said to be a parametrization

References

• https://en.wikipedia.org/wiki/Topological_manifold