nLab
locally closed set

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

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.

category: topology

Last revised on April 14, 2016 at 09:19:45. See the history of this page for a list of all contributions to it.