In the proof of Schauder fixed point theorem in Evans' PDE book, he uses a claim that the convex hull $K$ of $N$ points $x_1,\dots,x_N$ in a convex compact subset $A$ of a Banach space $X$ is homeomorphic to the closed unit ball in $\mathbb{R}^M$ with $M\leq N$. Can someone show me why or provide some reference on the proof of this claim?
2026-03-30 05:16:23.1774847783
Show homeomorphism between convex hull and unit ball?
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A simple Google search yields the following document:
http://relaunch.hcm.uni-bonn.de/fileadmin/geschke/papers/ConvexOpen.pdf
I am sure you can modify this method of proof to prove exactly what you want.