distinguished open sets

A form of distinguished open set — A particularly basic kind of set, generalizing the notion of the complement of a hypersurface, originating in the study of algebraic varieties but in modern mathematics also extending to the setting of affine schemes. Formally: (in the context of affine or projective varieties) the complement of the zero locus of a polynomial in affine or projective space; (in scheme theory) the subset of prime ideals of a commutative ring which do not contain some element of the ring.