EDB — 0WY

Exercises

1. [0WY] Let \(𝜑:[0,∞)→ [0,∞)\) be a function that is continuous in zero, monotonically weakly increasing and with \(𝜑(x)=0\iff x=0\). Show that \(\tilde d=𝜑◦ d\) is still an ultrametric. Show that spaces \((X,d)\) \((X,\tilde d)\) have the same topology.

   Compare with the exercise [0N1]↺↻, notice that we do not require \(𝜑\) to be subadditive.