It shouldn't. It starts off with metric spaces and Euclidean n-space. The main goal is to cover open and closed sets, convergence, and compactness. Why? Bec

It shouldn't. It starts off with metric spaces and Euclidean n-space. The main goal is to cover open and closed sets, convergence, and compactness. Why? Because those topics are crucial in continuity and uniform continuity. Why want those? Because continuous on a compact set means uniformly continuous and, thus, that the Riemann integral exists. Any questions?