In algebraic geometry, a universal homeomorphism is a morphism of schemes f : X → Y {\displaystyle f:X\to Y} such that, for each morphism Y ′ → Y {\displaystyle Y'\to Y} , the base change X × Y Y ′ → Y ′ {\displaystyle 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 algebraic geometry, a universal homeomorphism is a morphism of schemes f : X → Y {\displaystyle f:X\to Y} such that, for each morphism Y ′ → Y {\displaystyle Y'\to Y} , the base change X × Y Y ′ → Y ′ {\displaystyle 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.
Source: Wikipedia "Universal homeomorphism" · CC BY-SA 4.0
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