Covering spaces & lifting theorems

Question 1

covering map

Answer 1

continuous surjection such that each x has an open nhbd U for which p^-1(U) is a union of disjoint open sets S_i and p restricted to S_i is a homeomorphism

Question 2

lift

Answer 2

continuous map such that p f’ = f

Question 3

unique lifting property

Answer 3

Y connected
A={y in Y| f1(y)=f2(y)} is either empty or Y

Question 4

Path Lifting Theorem

Answer 4

there exists a unique lift of path

Question 5

Homotopy Lifting Theorem

Answer 5

there is unique lift of homotopy

Question 6

Homotopy lifting 2

Answer 6

if based homotopic paths then based homotopic lifts

Question 7

right action

Answer 7

identity and composition

Question 8

Ultimate Lifting Theorem

Answer 8

Y connected and locally path connected
f continuous
f has a lift iff
f_(π1(Y,y0)) is in p_(π1(E,e0))