First Year Topology Exam I Materials

TheseĀ  homeworks, review problems and exams will give you some idea of the kind of problems to expect.

Here is the material covered, Numbers in parentheses are section number from Munkres, Topology,
2nd edition. Some sections had just part covered.

  • Set Theory, algebra of set operations, functions, relations (1-5)
  • Cardinality (6,7)
  • Axiom of Choice and Zorn’s Lemma (9, 11)
  • Topological spaces, products, basis, metrics, quotients (12-22)
  • Connectedness, path connectedness, local propeties (25-25)
  • Compactness, limit point and sequential compactness (26-28)
  • One point compactification (Theorem 29,2)
  • 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)
  • Urysohn Lemma and Tietze Extension Theorem (33, 35)