Algebraic Topology - Lecture 8 - Galois Correspondence

[@GaloisCorr]

Showing the proof for the number of sheets was a bit sloppy. It is not clear to me how Elements of fundamental groups of different spaces can translate with each other. Using pi as both the covering map and the fundamental group is also confusing.
25:07

[@GaloisCorr]

Wouldn’t the induced homomorphism be used here as well? Thank you!