Editing Base (topology) (section)

===Objects defined in terms of bases===

* The [[order topology]] on a totally ordered set admits a collection of open-interval-like sets as a base.
* In a [[metric space]] the collection of all [[open ball]]s forms a base for the topology.
* The [[discrete topology]] has the collection of all [[singleton (mathematics)|singleton]]s as a base.
* A [[second-countable space]] is one that has a [[countable]] base.

The [[Zariski topology]] on the [[spectrum of a ring]] has a base consisting of open sets that have specific useful properties. For the usual base for this topology, every finite intersection of basic open sets is a basic open set.

* The [[Zariski topology]] of <math>\C^n</math> is the topology that has the [[algebraic set]]s as closed sets. It has a base formed by the [[set complement]]s of [[affine algebraic hypersurface|algebraic hypersurface]]s. 
* The Zariski topology of the [[spectrum of a ring]] (the set of the [[prime ideals]]) has a base such that each element consists of all prime ideals that do not contain a given element of the ring.