EDB — 0T7

Exercises

1. [0T7] Let \(A⊂ℝ^ n\) be a bounded set. For every \(\varepsilon {\gt}0\) there is a set \(I⊂ A\) that satisfies:

   • \(I\) is a finite set,

   • \(∀ x,y∈ I\), \(x≠ y\) you have \(x∉ B(y,\varepsilon )\) (i.e. \(d(x,y)≥ \varepsilon \)),

   • \[ A⊆ ⋃_{x∈ I} B(x,\varepsilon )~ ~ . \]
   Solution 1

   [0T8]↺↻