Originally Posted by

**thaopanda** I need help with this proof...

$\displaystyle d_{1},d_{2} : X \times X \rightarrow R$ distance on X are called equivalent provided that there exists $\displaystyle C_{1},C_{2}$ > 0 such that

$\displaystyle C_{2}d_{2}$(x,y) $\displaystyle \leq d_{1}$(x,y) $\displaystyle \leq C_{1}d_{2}$(x,y)

$\displaystyle \forall $x,y $\displaystyle \epsilon X$

Let $\displaystyle d_{1},d_{2}$ be equivalent distances on X and let $\displaystyle A \subseteq X$. Prove that A is open in $\displaystyle (X,d_{1})$ if and only if A is open in $\displaystyle (X,d_{2})$ (i.e. equivalent distancesgive the same open sets).

please help :(

Nicole