Separation axiom metaproperty chart

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Property T family name Hereditary Weakly hereditary Product-closed Refining-preserved Local
Kolmogorov T_0 Yes Yes Yes Yes Yes
T1 T_1 Yes Yes Yes Yes Yes
Hausdorff T_2 Yes Yes Yes Yes No
Urysohn T_{2.5} Yes Yes Yes Yes No
Regular T_3 Yes Yes Yes No No
Completely regular T_{3.5} Yes Yes Yes No No
Normal T_4 No Yes No No No
Hereditarily normal T_5 Yes Yes No No No
Perfectly normal T_6 Yes Yes  ?  ? No
Monotonically normal - Yes Yes  ?  ? No
Collectionwise Hausdorff - Yes Yes  ? Yes No