Definition 2

A topological space $X$ is said to be a Souslin space if it is metrizable and if there exists a Polish space $P$ and a continuous mapping of $P$ onto $X$. A subset $A$ of a topological space $X$ is called a Souslin set if the subspace $A$ is a Souslin space.

Clearly every Polish space is Souslin, and the image of a Souslin space $X$ under a continuous mapping of $X$ into a metrizable space $Y$ is a Souslin space.