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A topological space is T5 if it's both T1 and any two separated sets have disjoint open neighborhoods.

A topological space is T6 if it's both T1 and any two disjoint closed sets can be precisely separated by a continuous function.

A topological space is T3.5, or completely regular, if it's T1 and for any point and a closed set not containing it, there is a continuous function that separates them.

A topological space is T2.5 if any two distinct points can be separated by closed neighborhoods or if one point has a neighborhood that does not contain the other.

A topological space is completely Hausdorff if for every pair of distinct points, there exists a continuous function mapping the space into the real line such that the images of the points are distinct.

A topological space is T2, or Hausdorff, if for any two distinct points, there exist disjoint open sets each containing one of the points.

A topological space is T3 if it's both T0 and for any point and a closed set not containing it, there exist disjoint open sets each containing one of them.

A topological space is T4 if it's both T1 and any two disjoint closed sets have disjoint open neighborhoods.

A topological space is T0 if for any pair of distinct points, there is an open set containing one but not the other.