A subset $A$ of topological space $X$ is called a zero set if there exist continuous function $f:X \rightarrow \mathbb{R}$ such that $A=f^{-1} (\{0\})$. A cozero set is the complement of a zero set. A $\text{Coz}_\delta$ set is the countable intersection of cozero sets.
A nonempty set in a Hausdorff space is Souslin set when it can be represented as the image of the space $\mathbb{N}^{\mathbb{N}}$ under a continuous function. My question: Is it true that any $\text{Coz}_\delta$ set is Souslin set? Thank you.
What you call a Souslin set is also called an analytic set and all Borel sets are analytic. As zero sets are Borel, so are your countable intersections of cozero sets. So yes, if you want to use Borel sets are analytic, it's trivial.