EDB — 0Z1

Exercises

1. [0Z1] Topics:norm.Prerequisites:[109]↺↻.

   Let \(K\) be a compact in \(ℝ^ n\); we write \(\dim (K,|⋅|)\) to denote the limit that defines the dimension, using the balls of the Euclidean norm. Given a norm \(𝜙\) we can define the distance \(d(x,y)=𝜙(x-y)\), and with this calculate the dimension \(\dim (K,𝜙)\). Show that \(\dim (K,|⋅|)=\dim (K,𝜙)\), in the sense that, if one limit exists, then the other limit exists, and they are equal.

   Solution 1

   [0Z2]↺↻