EDB — 0R9

Exercises

1. [0R9]Topics:distance function.

   1. Show that \(d_ A\) is a Lipschitz function.

   2. Show that \(d_ A≡ d_{\overline A}\).

   3. Show that \(\{ x,d_ A(x)=0\} =\overline A\).

   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]↺↻