commutative algebra, the Zariski topology is a topology defined on geometric objects called varieties. It is very different from topologies that are commonly...

I{\text{ is an ideal of }}R\}.} This topology is called the Zariski topology. A basis for the Zariski topology can be constructed as follows. For f ∈...

prime ideals equipped with the Zariski topology, and the localizations of the ring at the open sets of a basis of this topology. This is the starting point...

to be open, this defines a topology (the Zariski topology) on CPn. Another construction of CPn (and its Zariski topology) is possible. Let S+ ⊂ S be...

Space-filling curve Topologist's sine curve Trivial topology Unit interval Zariski topology Counterexamples in Topology π-Base: An Interactive Encyclopedia of Topological...

topology and coarser than the strong topology. The complex vector space Cn may be equipped with either its usual (Euclidean) topology, or its Zariski...

simplex and every simplicial complex inherits a natural topology from . The Zariski topology is defined algebraically on the spectrum of a ring or an...

For the usual base for this topology, every finite intersection of basic open sets is a basic open set. The Zariski topology of C n {\displaystyle \mathbb...

defined in general. Less intuitive topologies are used in other branches of mathematics; for example, the Zariski topology, which is fundamental in algebraic...

an affine subvariety of kn the Zariski topology on V is simply the subspace topology inherited from the Zariski topology on kn. The geometric structure...