A subset of $\mathbb{R}^n$ is


* $G\_\delta$ if it is the intersection
of countably many open sets
* $F\_\sigma$ if it is the union of countably many closed sets
* $G\_{\delta\sigma}$ if it is the union
of countably many $G\_\delta$'s
* ...


This process gives rise to the [Borel hierarchy](https://en.wikipedia.org/wiki/Borel_hierarchy).


Since all closed sets are $G\_\delta$, all $F\_\sigma$ are $G\_{\delta\sigma}$. What is an explicit example of a $G\_{\delta\sigma}$ that is not $F\_\sigma$?



A G-delta-sigma that is not F-sigma?
Any dense $G\_{\delta}$ with empty interior is of II Baire category, and cannot be $F\_\sigma$ by the Baire theorem (and of course it is in particular a $G\_{\delta\sigma}$).


