Definition:Tychonoff Separation Axioms

Definition
The Separation Axioms (sometimes known as the Kolmogorov Separation Axioms or the Tychonoff Separation Axioms) are a classification system for topological spaces such that each condition is stronger than the predecessor; that is to say, a $T_2$ space is necessarily $T_1$ as well, but there exist $T_1$ spaces which are not $T_2$.

Apart from the ones below, other kinds of $T$ spaces have been defined, but these definitions vary from author to author.

For all of these definitions, $T = \left({X, \vartheta}\right)$ be a topological space with topology $\vartheta$.

Linguistic Note
The letter $T$ comes from the German Trennungsaxiom, which means separation axiom.