MTG 5316 Introduction to Topology 1

Numbers in parentheses are section numbers from James R. Munkres, Topology, 2nd edition. Some sections are only partly covered. Specifics may vary depending on the professor who taught the course or prepared 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, bases, metrics, quotients (12–22)
• Connectedness, path connectedness, local properties (23–25)
• Compactness, limit-point compactness, 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 of Section 43)
• Baire spaces and the Baire category theorem (48)