I have to prove that
equivalent distances define same topology.
I know there are similar questions, so please don't have a go at me but I am still confused and they don't answer it in the way I have been taught.
If distances are equivalent then there exist an $\alpha$ and $\beta$ more than zero such that $$\alpha d_1(x,y) \leq d_2(x,y) \leq \beta d_1(x,y)$$
Please help me