EDB — 0YZ

[0YZ] Prerequisites:[0N1]↺↻.Let $K\subseteq X$ compact; fix $𝛼>1$; define $\tilde{d}(x,y)=\sqrt[𝛼]{d(x,y)}$. We know from [0N1]↺↻ that it is a distance. Show that

In particular $K=[0,1]$ (the interval $K\subseteq X=ℝ$) with the distance $\tilde{d}(x,y)=\sqrt[𝛼]{|x-y|}$ has dimension $𝛼$.