Copyied from "Real Analysis" (H.L. Royden):
These are topological spaces.
T_{1}: Given two distinct points x and y, there is an open set which contains y but not x.
T_{2}: Given two distinct points x and y, there are disjoint open sets O_{1} and O_{2} such that x\in O_{1} and y\in O_{2}.
T_{3}...