EDB — 12T

Exercises

1. [12T]Prerequisites:[124]↺↻.

   Recall that the operation \(A ∙ B=(A⊕B)⊖B\) is called ”closing”.

   • Show that \(A ⊆ A ∙ B\).

   • Let \(X=ℝ^ n\), \(B=B_ r=\{ \| x\| {\lt} r\} \) a ball, find an example of a set \(A\) that is open non-empty bounded, and \(A ∙ B=A\).

   • Setting \(X=ℝ^ n\), \(B=B_ r\) a ball, find an example where \(A ∙ B≠ A\).

   Solution 1

   [12V]↺↻