Because of boundary points, I can sort of see intuitively why Euclidean half-space, i.e. {(x_1, ... , x_n) : x_n >= 0} is not a manifold, but is there a simple rigorous argument for why Euclidean half-space is not homeomorphic to an open set of R^n. I do not know too much topology and the topological properties I am familiar with (e.g. compactness, connectedness, fundamental group) are the same for both spaces.
Thanks.
Thanks.