I'm given two distances that are defined on some metric space and I need to show that open sets and Cauchy sequences coincide for the two distances. What does this mean? I'm avoiding giving details on purpose, but a nice definition would help :)
I found that for two distances to be equivalent we need $\exists$ $0<c_1<c_2<\infty$ s.t. $c_1< d_1/d_2< c_2$, but in my particular case I can't find a particular lower bound.