Constructible subset of a variety

A constructible subset is a finite union of locally closed subsets in the Zariski topology. A dense constructible subset contains a dense open subset. Constructibility alone is weaker than closedness, but a constructible subgroup is closed.

The image of a morphism of algebraic varieties is constructible. This replaces the generally false assertion that all morphisms have closed image. Group structure adds the fact that a constructible subgroup is closed.