1. The problem statement, all variables and given/known data Prove: a topological group is discrete if the singleton containing the identity is an open set. The statement is in here http://en.wikipedia.org/wiki/Discrete_group 3. The attempt at a solution Is that because if you multiply the identity with any element in the group, you get a new element with nothing surrounding it because it's like you can also multiply the area around the identity to the new position. In other words mapping open sets to open set? f is cts => open sets are mapped to open sest in a topological group.