I'm trying to prove the following Theorem. Suppose T1 and T2 are topologies for X. The following are equivalent: 1. T1 is a subset of T2; 2. if F is closed in (X, T1), then F is closed in (X, T2); 3. if p is a limit point of A in (X, T2), then p is a limit point of A in (X, T1). So far, I've shown 1 implies 2. However, I'm curious about the reversal of T1 and T2 in statements 2 and 3. Is there a typo? I'm tying to show 1 implies 3, but I'm having no luck. I'll try reversing statement 3 and seeing if that works. If anyone thinks that there is a typo, please let me know. Thanks!