Editing Covering group (section)

{{Use American English|date = March 2019}}
{{Short description|Concept in topological group theory}}
{{about|topological covering group|algebraic covering group|universal perfect central extension}}
In [[mathematics]], a '''covering group''' of a [[topological group]] ''H'' is a [[covering space]] ''G'' of ''H'' such that ''G'' is a topological group and the covering map {{nowrap|''p'' : ''G'' → ''H''}} is a [[continuous (topology)|continuous]] [[group homomorphism]]. The map ''p'' is called the '''covering homomorphism'''. A frequently occurring case is a '''double covering group''', a [[double cover (topology)|topological double cover]] in which ''H'' has [[Index of a subgroup|index]] 2 in ''G''; examples include the [[spin group]]s, [[pin group]]s, and [[metaplectic group]]s.

Roughly explained, saying that for example the metaplectic group Mp<sub>2''n''</sub> is a ''double cover'' of the [[symplectic group]] Sp<sub>2''n''</sub> means that there are always two elements in the metaplectic group representing one element in the symplectic group.