1. The problem statement, all variables and given/known data Suppose that [tex]f : (X,d_X) \to (Y,d_Y)[/tex]. If [tex]f[/tex] is continuous, must it map open sets to open sets? If [tex]f[/tex] does map open sets to open sets must [tex]f[/tex] be continuous? 2. Relevant equations 3. The attempt at a solution The answer to the first question is yes. The answer to the second question I guess is "no". Is this correct? How can I prove it?