I just started reading a textbook, and it keeps saying that an $n$-dimensional manifold is a topological space with the same local properties as Euclidean $n$-space.
I don't really understand what is meant by "local properties." What what would be an example for, say, a $2$-dimensional manifold that is not a Euclidean $2$-space like $\mathbb{R}^2$ or something, but still has the "local properties" of the Euclidean space?