A list of five properties of a topological space X expressing how rich the "population" of open sets is. More precisely, each of them tells us how tightly a closed subset can be wrapped in an open set. The measure of tightness is the extent to which this envelope can separate the subset from other subsets. The numbering from 0 to 4 refers to an increasing degree of separation. 0. T_0-separation axiom: For any two points x, y element X, there is an open set U such that x element U and y not element U or y element U and x not element U. 1. T_1-separation axiom: For any two points x, y element X there exists two open sets U and V such that x element U and y not element U, and y element V and x not element V.

T_0-separation axiom | T_0-space | T_1-separation axiom | T_1-space | T_2-separation axiom | T_2-space | T_3-separation axiom | T_3-space | T_4-separation axiom | T_4-space