The topic of this course is the fundamental group and covering spaces. Here are recommended books (the order is random):
Massey: Basic course in algebraic topology (or Algebraic topology, an introduction)
Munkres: Topology 2nd edition (The first edition does not include our material)
Bredon: Topology and geometry
Hatcher: Algebraic topology (appears at
Singer and Thorpe: Lecture notes on elementary topology and geometry
Lawson: Topology, a geometric approach
Our procedure for defining homotopies on quotient spaces is justified by Theorem 20.1 of Munkres - Elements of Algebraic Topology. Take C to be the unit interval I, which is indeed locally compact and Hausdorff.
We will discuss the homework in the second half of class on the following dates: 11.11.20, 25.11.20, 9.12.20, 23.12.20, 6.1.21, 20.1.21.

HW1 (to be done by 28.10.20)
HW2 (to be done by 4.11.20)
HW3 (to be done by 11.11.20)
HW4 (to be done by 18.11.20)
HW5 (to be done by 25.11.20)
HW6 (to be done by 2.12.20)
HW7 (to be done by 9.12.20)
HW8 (to be done by 16.12.20)
HW9 (to be done by 23.12.20)
HW10 (to be done by 30.12.20)
HW11 (to be done by 6.1.21)
HW12 (to be done by 13.1.21)
HW13 (to be done by 20.1.21)