My question concerns the $F_\sigma$ property of a topological space $X$. I want to know if there is a particular name for those spaces in which every open set is $F_\sigma$.
Moreover, if $X$ is a metric space the the above property is true, however, what happens if we ask less regularity from the space? Myabe only the axioms of countability can guarantee it?
Also, any reference on the subject is appreciated.