The homeomorphic image of a so-called "complete separable" metric space. The continuous image of a Polish space is called a Souslin set.
Polish Space
See also
Descriptive Set Theory, Standard SpaceExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Polish Space." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PolishSpace.html