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Dec 13, 2018 at 15:19 comment added David E Speyer Whoops! You are right, of course.
Dec 13, 2018 at 15:11 comment added fedja @DavidESpeyer You meant $1\le x+y \le 2$, right?
Dec 13, 2018 at 14:42 comment added David E Speyer Note also that the same example works on $K = \{ 0 \leq x,y,\ x+y \leq 1 \}$, so requiring that $K$ be full dimensional doesn't help.
Dec 13, 2018 at 13:01 history answered fedja CC BY-SA 4.0