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T0 space A topological space X such that, for any two distinct points of X, there is a neighborhood of one which does not contain the other. That is, for all x, y in X, with x = y, there is an open set U such that either x ∈ U and y /∈ U , or y ∈ U and x /∈ U . T0 spaces are also known as Kolmogorov spaces.