Universal homeomorphism

In algebraic geometry, a universal homeomorphism is a morphism of schemes $$f: X \to Y$$ such that, for each morphism $$Y' \to Y$$, the base change $$X \times_Y Y' \to Y'$$ is a homeomorphism of topological spaces.

A morphism of schemes is a universal homeomorphism if and only if it is integral, radicial and surjective. In particular, a morphism of locally of finite type is a universal homeomorphism if and only if it is finite, radicial and surjective.

For example, an absolute Frobenius morphism is a universal homeomorphism.