A connected Lie group G has a universal covering group G̃. The covering homomorphism σ:G̃→ G is typically not one-to-one. A map from G back into G̃ is called a lift if its composition with σ is the identity map on G. If σ is not one-to-one, then a lift cannot be continuous everywhere, but any continuous path γ in G can be lifted to a continuous path γ̃ in G̃ with σ(γ̃)=γ. This article introduces a special lift and applies it to the idea of lifting a practically continuous path (sequence of closely-spaced points) in G to a practically continuous path in G̃. Article 40191 uses this to define Wilson operators associated with representations of the covering group G̃ of the gauged group G.
