Topological properties diagram

The diagram below shows which topological properties imply which others.

Here is the GraphViz file used to create the diagram.

Hausdorff, Lindelöf, collectionwisenormal, compact, secondcountable, metrizable, completelyregular, paracompactHausdorff, metrizable, normal, regular, separable, stronglyparacompact


Some of the implications in the diagram are trivial. If a space satisfies conditions A and B then obviously it satisfies B. These trivial implications are included for the sake of further implications that may only depend on B.

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