Editing Normal space (section)

== Examples of non-normal spaces ==
An important example of a non-normal topology is given by the [[Zariski topology]] on an [[algebraic variety]] or on the [[spectrum of a ring]], which is used in [[algebraic geometry]].

A non-normal space of some relevance to analysis is the [[topological vector space]] of all [[function (mathematics)|function]]s from the [[real line]] '''R''' to itself, with the [[topology of pointwise convergence]].
More generally, a theorem of [[Arthur Harold Stone]] states that the [[product topology|product]] of [[uncountable|uncountably many]] non-[[compact space|compact]] metric spaces is never normal.