MTG 5317 Introduction to Topology 2

  1. Compactness of products. Tychonoff theorem (formulation). Baire category theorem (now for compact spaces).
  2. Homotopy of maps, homotopy equivalence of spaces, retraction and deformation retraction. Contractible spaces, examples. Homotopy path, loops.
  3. Fundamental group, homotopy invariance, the role of the base point. Fundamental group of the circle. Non-contractibility of the circle. Brouwer fixed point theorem for the 2-disk.