Noun
Zariski topology (plural Zariski topologies)
(algebraic geometry) Originally, a topology applicable to algebraic varieties, such that the closed sets are the variety's algebraic subvarieties; later, a generalisation in which the topological space is the set of prime ideals of a commutative ring and is called the spectrum of the ring.
The Zariski topology allows tools from topology to be used in the study of algebraic varieties, even when the underlying field is not a topological field.
A basis for the Zariski topology can be constructed as follows. Source: Internet
The Zariski topology on Sch is generated by the pretopology whose covering families are jointly surjective families of scheme-theoretic open immersions. Source: Internet
If one only considers the points of A, i.e. the maximal ideals in R, then the Zariski topology defined above coincides with the Zariski topology defined on algebraic sets (which has precisely the algebraic subsets as closed sets). Source: Internet
The gluing is along Zariski topology; one can glue within the category of locally ringed spaces, but also, using the Yoneda embedding, within the more abstract category of presheaves of sets over the category of affine schemes. Source: Internet