Editing Metrizable space (section)

{{short description|Topological space that is homeomorphic to a metric space}}
{{inline citations|date=September 2024}}
In [[topology]] and related areas of [[mathematics]], a '''metrizable space''' is a [[topological space]] that is [[Homeomorphism|homeomorphic]] to a [[metric space]]. That is, a topological space <math>(X, \tau)</math> is said to be metrizable if there is a [[Metric (mathematics)|metric]] <math>d : X \times X \to [0, \infty)</math> such that the topology induced by <math>d</math> is <math>\tau.</math><ref>{{cite web|last=Simon|first=Jonathan|title=Metrization Theorems|url=http://homepage.math.uiowa.edu/~jsimon/COURSES/M132Fall07/MetrizationTheorem_v5.pdf|access-date=16 June 2016}}</ref><ref>{{cite book|last=Munkres|first=James|author-link=James Munkres|title=Topology|year=1999|publisher=[[Pearson PLC|Pearson]]|page=119|edition=second}}</ref> ''Metrization theorems'' are [[theorem]]s that give [[sufficient condition]]s for a topological space to be metrizable.