Definition talk:T3 Space

Names of the separation axioms

Is there a way to change normal with T4 and regular with T3 and so on? I think is much better to choose that nomenclature so that we have theorems like $T5\implies T4\implies T3\implies T2\implies T1\implies T0$ and "completely regular $\implies$ regular". --Dan232 17:36, 20 August 2011 (CDT)

Good question, I'll try to answer it adequately. Unfortunately I don't agree. Sorry, but we can't change it at this stage. Besides, I think it is much better to choose the nomenclature that the Tn goes with the simple properties, and let the chain of implications look after itself. That chain is far more complicated than just a simple linear list of arrows - take a look at Sequence of Implications of Separation Axioms for a look at it in its full glory.

There's a page on PlanetMath which analyses the literature (or some of it) and it's split about 50-50 as to which way the proverbial cat is made to jump. We (i.e. I) picked one, that's the one we stick with. There is adequate comment in the appropriate pages referring to the other way of doing it.

The main source work I followed when I put this lot together was (as you have probably surmised) 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) which does a comprehensive analysis (if occasionally flawed) of this area, and I have not been able to find anything on line that comes close (Wikipedia falls short in several places). It transpires that $\mathsf{Pr} \infty \mathsf{fWiki}$ now appears to be the definitive source work, for it now includes the proofs that are missing from Steen and Seebach.

So, as I say, this is the nomenclature adopted, and unless more cogent reasons than "I prefer it the other way" can be found, this is how it will stay. --prime mover 17:58, 20 August 2011 (CDT)

I just found rough to follow which axioms implicates which, but with the link Sequence of Implications of Separation Axioms is much clearer, thank you. --Dan232 18:31, 20 August 2011 (CDT)