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MTG 5316 Introduction to Topology 1

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

  • Set Theory, algebra of set operations, functions, relations (1-5)
  • Cardinality (6,7)
  • Axiom of Choice, Well-ordered sets and Zorn’s Lemma (9-11)
  • Topological spaces, products, basis, metrics, quotients (12-22)
  • Connectedness, path connectedness, local propeties (23-25)
  • Compactness, limit point and sequential compactness (26-28)
  • One point compactification (Theorem 29,1)
  • Countability and separation axioms (30-32)
  • Complete metric spaces, spaces of functions with the uniform and sup topologies (43)
  • Contraction mapping theorem (exercise 7 of section 28 and exercise 5 from section 43)
  • Baire spaces and the Baire Category Theorem (48)