Separation axiom metaproperty chart

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