A topological space \(X\) is locally Euclidean of dimension \(n\) if and only if every point has a neighbourhood in \(X\) which is homeomorphic to an open ball in \(\mathbb{R}^n\) or to \(\mathbb{R}^n\) itself. [1, Lemma 2.52]

References Link to heading

1. J. Lee, Introduction to Topological Manifolds. New York, NY: Springer New York, 2011. doi:10.1007/978-1-4419-7940-7