Give example of a set $X$ and two metrics $d_1,d_2$ on $X$ such that $(X,d_1)$ and $(X,d_2)$ are topologically equivalent but there exist a function $f:X \to X$ which is uniformly $d_1$ continuous but not uniformly $d_2$ continuous . What I know is that the metrics cannot be strongly equivalent . Please help . Thanks in advance
-
$\begingroup$ I think it's just "metrics" and not "metrices" ;) $\endgroup$ – Math1000 Feb 28 '15 at 14:26
-
$\begingroup$ @Math1000 : I will edit :) $\endgroup$ – user217921 Feb 28 '15 at 14:28