Non-Hausdorff Spaces

Topology · Axiom Academy

Three worked examples of topological spaces that fail the Hausdorff separation axiom A topological space is Hausdorff if for any two distinct points , there exist disjoint open sets such that . A space is non-Hausdorff if there exist at least two distinct points that cannot be separated by disjoint open sets. Example 1: The Line with Two Origins Example 2: Cofinite Topology on an Infinite Set Example 3: The Indiscrete Topology Based on the example above, which approach is correct?

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