Algebraic Topology - 2 - Balls

Here we show that convex sets in RR^n which are compact with nonempty interior are homeomorphic to the n-ball --- the boundaries are (n-1)-spheres.

Errata:
In the one point compactification we need open neighborhoods of infinity to have compact complement. So a neighborhood at infinity is of the form K^c \cup \lbrace \infty \rbrace where K \subset X is compact.

[HanBurritoz]

6:11 Don't you mean 'for U compact in X'?