  We prove that any finite-degree polynomial functor is topologically
Noetherian. This theorem is motivated by the recent resolution of Stillman's
conjecture and a recent Noetherianity proof for the space of cubics. Via work
by Erman-Sam-Snowden, our theorem implies Stillman's conjecture and indeed
boundedness of a wider class of invariants of ideals in polynomial rings with a
fixed number of generators of prescribed degrees.
