I am looking for the name and notation of the following separation axiom , temporarily denoted by $T_i$ (where $i=\sqrt{-1}$ is the imaginary unit):

** Axiom $T_i$**: For any point $x$ of a topological space $X$ and any neighborhood $O_x$ of $x$ there is a closed subset $F$ in $X$ that contains $x$ and is contained in $O_x$.

It is easy to see that a topological space $X$ satisfies the axiom $T_i$ if and only if *each open set in $X$ is a union of closed sets*.

It is easy to check that the separation axiom $T_1$ is equivalent to $T_0+T_i$.

The connected doubleton is an example of a $T_0$-space which is not $T_i$. Any anti-discrete space satisfies $T_i$ but not $T_0$. So, the axioms $T_0$ and $T_i$ are incomparable.

**Question**: Is the axiom $T_i$ known? If yes, where is it introduced and how is it denoted and called?