# Existence of Topological Space which satisfies no Separation Axioms but T0

## Theorem

There exists at least one example of a topological space for which none of the Tychonoff separation axioms are satisfied except for the $T_0$ (Kolmogorov) axiom.

## Proof

Let $T$ be the overlapping interval space.

From Overlapping Interval Space fulfils no Separation Axioms but $T_0$, we have that $T$ satisfies none of the Tychonoff separation axioms except for the $T_0$ (Kolmogorov) axiom.

$\blacksquare$