Universal homeomorphism explained

f: X \to Y such that, for each morphism Y' \to Y , the base change X x _{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.^[1] 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.

External links

• Universal homeomorphisms and the étale topology
• Do pushouts along universal homeomorphisms exist?

Notes and References

1. EGA IV₄, 18.12.11.