T0: Because T 1 and T 1 are similar and easy to be confused, I want to point out that the difference of T 1 is that not two open sets can be constructed for two points, but only one of the two points can be separated. Obviously, T 1 is T0, and the right topology T 1 is not T 1, which is a good counterexample. You might as well understand.
T2: Two open sets can be constructed for two points, so that each open set contains only one point and the two open sets do not intersect.
T3: Regularity is the same as T0 and T2, but it separates a closed set from a point, that is, two open sets can be found, one contains only closed sets and the other contains only points, and the two open sets do not intersect.
T4: normal and T 1, as above, two open sets can be found to separate two closed sets.