Definition:Tychonoff Separation Axioms

Definition
The Tychonoff separation axioms are a classification system for topological spaces.

They are not axiomatic as such, but they are conditions that may or may not apply to general or specific topological spaces. In general, each condition is stronger than the previous one, with subtleties.

For all of these definitions, $T = \struct {S, \tau}$ is a topological space with topology $\tau$.

Also known as
The Tychonoff separation axioms are also known as the Tychonoff conditions.

Some sources refer to them as just the separation axioms.

Some sources call them the $T_i$ axioms or just $T$-axioms.

Also see

 * Sequence of Implications of Separation Axioms