Covering

Universal covering

The universal covering is a covering with a simply connected covering space . homotopy It follows immediately that the characteristic subgroup of is trivial, and by deck transformation group of a regular covering as quotient

for any . The universal covering is universal in the sense that is the initial object of the category of pointed connected coverings , assuming is locally path-connected.

Properties

• The universal covering is regular.
• Main theorem of coverings
• A locally path-connected, connected space is semilocally simply connected iff it has a universal covering.

---

develop | en | sembr