Definition:Tychonoff Separation Axioms/Naming Conventions

Naming Conventions for Tychonoff Separation Axioms

There are different ways of naming the Tychonoff separation axioms.

The technique for $\mathsf{Pr} \infty \mathsf{fWiki}$ is to follow the convention used in 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.).

Beware: this differs from the Separation axiom page at Wikipedia.

The various naming schemes are inconsistent with each other and confusing, and no completely satisfactory convention has been defined.

It is suggested that the system used here is more modern than others, but there is little evidence one way or another.

An attempt has been made on the appropriate pages to mention the alternative names of these spaces, but this is inconsistent and possibly inaccurate.

The important things to note are:

the conditions themselves

and:

the relations between them.

This is a new area of mathematics in which research is ongoing, and the whole area of ground may shift again completely in the near future.

Sources

• 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $2$: Separation Axioms: Regular and Normal Spaces