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  "body": "\n## Summary\n\nThe Kolmogorov quotient of a topological space identifies any two points that no open set can tell apart.\nThe result is a [[T0 space|07SG12TQH3]], and its open sets correspond exactly to the open sets of the original space.\nIt lets one pass to a $T_0$ space without losing any topological information.\nFor a pseudometric space it gives the associated metric space.\n\n## Explanations\n\n### L1 human\n\nIn some spaces, two different points have exactly the same neighbourhoods.\nNo open set contains one of them without the other, so the topology cannot see the difference.\nThe Kolmogorov quotient glues such twin points into one point.\nFor example, on $\\R^2$ with the pseudometric $d((x_1, y_1), (x_2, y_2)) = \\abs{x_1 - x_2}$, points on the same vertical line are twins.\nGluing them gives the real line.\n",
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