Universal homeomorphism

In algebraic geometry, a universal homeomorphism is a morphism of schemes $f:\; X\; \backslash to\; Y$ such that, for each morphism $Y\text{'}\; \backslash to\; Y$, the base change $X\; \backslash times\_Y\; Y\text{'}\; \backslash to\; Y\text{'}$ is a homeomorphism of topological spaces.

A morphism of schemes is a universal homeomorphism if and only if it is integral, radicial and surjective.EGA IV₄, 18.12.11. 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.