Poincare Project: More on Separation Axioms
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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Created: Jan. 29, 2005
Last Modified: Feb. 8, 2005
Author: jtauber
Last Modified: Feb. 8, 2005
Author: jtauber