EDB — 107

Exercises

1. [107] Prerequisites:[0PS]↺↻.Let $X$ be a vector space, let $𝜙,𝜓$ be two norms on it. Show that the topologies generated by $𝜙$ and $𝜓$ coincide, if and only if there exist $0<a<b$ such that

   $$\begin{array}{}\text{(1)}& \forall x,a𝜓(x)\le 𝜙(x)\le b𝜓(x).\end{array}$$

   3

   (When the relation ?? holds, we will say that the norms are ”equivalent”).

   Solution 1

   [108]↺↻