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*.

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.