EDB — 0YZ

[0YZ] Prerequisites:[0N1]↺↻.Let \(K⊆ X\) compact; fix \(𝛼{\gt}1\); 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 \(K⊆ X=ℝ\)) with the distance \(\tilde d(x,y)=\sqrt[𝛼]{|x-y|}\) has dimension \(𝛼\).