Relationships To Other Separation Axioms
If a normal space is R0, then it is in fact completely regular. Thus, anything from "normal R0" to "normal completely regular" is the same as what we normally call normal regular. Taking Kolmogorov quotients, we see that all normal T1 spaces are Tychonoff. These are what we normally call normal Hausdorff spaces.
Counterexamples to some variations on these statements can be found in the lists above. Specifically, Sierpinski space is normal but not regular, while the space of functions from R to itself is Tychonoff but not normal.
Read more about this topic: Normal Space
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