1. The problem statement, all variables and given/known data can someone help me to solve these problems in details?? Consider A =(0,1)× R. Is A open w.r.t. the topology induced by the French railway metric in R2? how about B=(-1,1)× R??? 2. The attempt at a solution I know A is open in the topology induced by d if and only if U is a union of metric balls. But for my questions here, how can I see that A is a union of metric balls?? should I take any x in A then exists r>0 s.t. B(x,r) is open in A?but now the French railway metric gives me 2 different cases, how to consider????