T2 is the weakest separation axiom that implies Hausdorffness.

In a T0 space, points are not necessarily open or closed.

In a T1 space, every point is either open or closed, but not both.

T2 is the weakest separation axiom that implies Hausdorffness, which means that every two distinct points can be separated by open sets.

T3 is the weakest separation axiom that implies regularity, which means that every two distinct points can be separated by open sets, and every closed set is a Gδ set.

T4 is the strongest separation axiom, and it implies that every two distinct points can be separated by open sets, every closed set is a Gδ set, and every point is a Gδ set.

The Sorgenfrey line is a T0 space that is not a T1 space because it contains points that are neither open nor closed.

The Cantor set is a T1 space that is not a T2 space because it contains points that cannot be separated by open sets.

The Sierpinski space is a T2 space that is not a T3 space because it contains closed sets that are not Gδ sets.

The real line with the usual topology is a T3 space that is not a T4 space because it contains points that are not Gδ sets.

The real line with the usual topology is a T4 space because it satisfies all of the separation axioms.

The Sierpinski space is not a T0 space because it contains points that are neither open nor closed.

The Cantor set is not a T1 space because it contains points that are neither open nor closed.

The Sierpinski space is not a T2 space because it contains points that cannot be separated by open sets.

The Sierpinski space is not a T3 space because it contains closed sets that are not Gδ sets.