Editing Normal space (section)

== Relationships to other separation axioms ==
If a normal space is [[R0 space|R<sub>0</sub>]], then it is in fact [[completely regular]].
Thus, anything from "normal R<sub>0</sub>" to "normal completely regular" is the same as what we usually call ''normal regular''.
Taking [[Kolmogorov quotient]]s, we see that all normal [[T1 space|T<sub>1</sub> space]]s are [[Tychonoff space|Tychonoff]].
These are what we usually call ''normal Hausdorff'' spaces.

A topological space is said to be [[pseudonormal space|pseudonormal]] if given two disjoint closed sets in it, one of which is countable, there are disjoint open sets containing them. Every normal space is pseudonormal, but not vice versa.

Counterexamples to some variations on these statements can be found in the lists above.
Specifically, [[Sierpiński space]] is normal but not regular, while the space of functions from '''R''' to itself is Tychonoff but not normal.