We previously defined types of topological spaces called T_0, T_1 and T_2 spaces. I've tried below to capture the distinction between them informally with a diagram.

Recall that a topological space is:

- T_0 iff for every pair of points x, y there is an open set U such that
*either*x is in U but y is not*or*y is in U but x is not. - T_1 iff for every pair of points x, y there are open sets U and V such that x is in U but y is not
*and*y is in V but x is not. - T_2 iff for every pair of points x, y there are open sets U and V such that x is in U, y is in V
*and*U and V are disjoint.

**UPDATE**: next post

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The original post was in the category: poincare_project but I'm still in the process of migrating categories over.