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MTG 5317 Introduction to Topology 2

Numbers in parentheses are section number from Munkres, Topology, 2nd edition. Some sections are only partly covered. Some specifics may vary depending on the Professor who taught the course and/or is making up the exam

  • Urysohn Lemma and Tietze Extension Theorem (33, 35)
  • Tychonoff Theorem (37)
  • Stone-Čech compactification (38)
  • Path homotopy  and the fundamental group (51, 52)
  • Covering spaces (introduction)  and the Fundamental group of the circle (53, 54)
  • Retractions, fixed points, and the Borsuk-Ulam Theorem (55, 57)
  • Deformation retract and homotopy (58)
  • Fundamental group of spheres (59)
  • Fundamental group of some surfaces (60)
  • Algebraic preliminaries to SVK theorem (67-69)
  • The SVK- push out, classical and generator/relation versions (70)
  • Fundamental group of wedge of circles, the torus, the dunce cap, the projective plane (71, 73, 74)
  • Abelianization of fundamental group (first Homology) (75)