Editing General topology (section)

====Further examples====
* There exist numerous topologies on any given [[finite set]]. Such spaces are called [[finite topological space]]s. Finite spaces are sometimes used to provide examples or counterexamples to conjectures about topological spaces in general.
* Every [[manifold]] has a [[natural topology]], since it is locally Euclidean.  Similarly, every [[simplex]] and every [[simplicial complex]] inherits a natural topology from '''R'''<sup>n</sup>.
* The [[Zariski topology]] is defined algebraically on the [[spectrum of a ring]] or an [[algebraic variety]].  On '''R'''<sup>''n''</sup> or '''C'''<sup>''n''</sup>, the closed sets of the Zariski topology are the [[solution set]]s of systems of [[polynomial]] equations.
* A [[linear graph]] has a natural topology that generalises many of the geometric aspects of [[graph theory|graph]]s with [[Vertex (graph theory)|vertices]] and [[Graph (discrete mathematics)#Graph|edges]].
* Many sets of [[linear operator]]s in [[functional analysis]] are endowed with topologies that are defined by specifying when a particular sequence of functions converges to the zero function.
* Any [[local field]] has a topology native to it, and this can be extended to vector spaces over that field.
* The [[Sierpiński space]] is the simplest non-discrete topological space.  It has important relations to the [[theory of computation]] and semantics.
* If Γ is an [[ordinal number]], then the set Γ = [0,&nbsp;Γ) may be endowed with the [[order topology]] generated by the intervals (''a'',&nbsp;''b''), [0,&nbsp;''b'') and (''a'',&nbsp;Γ) where ''a'' and ''b'' are elements of Γ.