EDB — 0R9

Exercises

1. [0R9]Topics:distance function.

   1. Show that $d_A$ is a Lipschitz function.

   2. Show that $d_A\equiv d_{\bar{A}}$.

   3. Show that $\{x,d_A(x)=0\}=\bar{A}$.

   4. If $M={ℝ}^n$ and $A$ is closed and non-empty, show that the infimum in [(9.62)]↺↻ is a minimum.

   See also [198]↺↻ and [19B]↺↻.

   Solution 1

   [0RB]↺↻