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For questions involving the concept of convexity

2 votes

Is every face exposed if all extreme points are exposed?

I believe I found a counterexample. We first set $d=3$ and $$ C_1:=B_1(0)\cup [0,1]\times [-1,1]\subset \mathbb R^2 \\ C_2:=C_1\times [-1,1]\subset \mathbb R^3, $$ where $B_1(0)$ denotes the closed un …
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