In algebraic geometry, a universal homeomorphism is a morphism of schemes such that, for each morphism , the base change 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.