The Galois correspondence in topology
Galois theory is really a general principle in pure mathematics. In this video we illustrate this by showing how there is a Galois correspondence in topology which is dual to the Galois correspondence that we see in field theory. In doing so, we introduce the notion of intermediate covers, which are the analogues of intermediate fields in classical Galois theory. The topological theory is a little more subtle, and we need also introduce the notion of simply connectedness and semi locally simply connected. This allows us to state the Galois correspondence between intermediate covers of a Galois covering map, and subgroups of the Galois group.