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wonderful so lets look over what we did last time so last time we were going back to covering spaces so going back to how we originally computed the fundamental group of the circle and we said that covering spaces are maps for which X has an open cover with every element of this cover evenly covered by P all right so ie open sets open subsets u P inverse of U is the disjoint union of a bunch of sets V and P restricted to any one of these as a homeomorphism okay and then we spend some time talking about how covering maps have important lifting properties right so the general case corresponds to when you have some map into a SpaceX and then you have a lift sorry you have a cover of that space X by X tilde and you want to know when is there lift and what we saw is that you always have necessary that the image of the fundamental group of Y under F be inside the image of the fundamental group of X tilde with respect to P and if Y is path connected and locally path connected then this is a