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Hausdorff space

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A topological space is called Hausdorff if we can "separate" any two points from each other by means of disjoint open sets: for any $x,y∈X, x≠y$, there are open sets $U, V$ such that $x∈U, y∈V$ and $U ∩ V = ∅.$

For more see separation axioms.