Editing Ramification (mathematics) (section)

{{Short description|Branching out of a mathematical structure}}
{{Other uses|Ramification (disambiguation){{!}}Ramification}}
[[Image:Schematic depiction of ramification.svg|right|thumb|300px|Schematic depiction of ramification: the fibers of almost all points in ''Y'' below consist of three points, except for two points in ''Y'' marked with dots, where the fibers consist of one and two points (marked in black), respectively. The map ''f'' is said to be ramified in these points of ''Y''.]]
In [[geometry]], '''ramification''' is 'branching out', in the way that the [[square root]] function, for [[complex number]]s, can be seen to have two ''branches'' differing in sign. The term is also used from the opposite perspective (branches coming together) as when a [[covering map]] [[degeneracy (mathematics)|degenerates]] at a point of a space, with some collapsing of the fibers of the mapping.