I've been reading GTM$202$: Introduction to Topological Manifolds these days, and in Chapter $1$, the author declared that open sets in $\mathbb{R}^n$ are manifolds for obvious reasons.
The book only defines a manifold as a subset of $\mathbb{R}^n$ which is locally Euclidean (which means you can always find a neighborhood isomorphic to a ball in Euclidean space for any given $x$ in this set). I don't think this proposition is obvious for me. Is there an intuitive way to convince people that this proposition is true? Or it is just another example of "Mathematical Obvious"?
Thanks for your answer in advance！