A set in a Polish space is a Borel set iff it is both analytic and coanalytic.
For subsets of 
,
a set is 
iff it is "hyperarithmetic."
Suslin's Theorem
See also
Analytic Set, Borel Set, Coanalytic Set, Polish SpaceExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Suslin's Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SuslinsTheorem.html