nLab locally closed set

A subset $A$ of a topological space $X$ is locally closed if it is a closed subset of an open subspace of $X$. Equivalently, every point in $A$ has a neighborhood $U\subset X$ such that $A\cap U$ is closed in $U$.

A locally closed subset for the Zariski topology on an affine space over an algebraically closed field is called an (embedded) quasiaffine variety, and a locally closed subset for the Zariski topology on a projective space over an algebraically closed field is called an (embedded) quasiprojective variety.

Related entries

• locally closed subtopos

category: topology