Prove that $[0,\infty)$ is not a manifold.
Using diffeomorphisms and the implicit function theorem perhaps.
A topological manifold is a space that looks locally like $\mathbb R^n$. Does $0$ in $[0, \infty)$ look like a point in $\mathbb R$?
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
3 years ago