Math 551 - Elementary Topology

• Prerequisites: Math 234.
• Frequency: Fall (I), Spring (II)
• Student Body: Math majors and graduate students in related areas
• Credits: 3. (N-A)
• Recent Texts: James R. Munkres: Topology, Second Edition
• Course Coordinator: Peter Orlik
• Background and Goals: This is an introduction to the basic ideas and methods of point set topology. It is a good background for analysis courses and graduate topology courses. Normally it is advisable to have at least one previous proof-based course such as Math 341, Math 421, Math 521 or Math 541 before taking Math 551.
• Alternatives: N/A
• Subsequent Courses: Math 552.

Content coverage:

• Elementary Set Theory: Sets, Cartesian products, equivalence relations, countability, the real line
• Basic Topology: metric spaces, topological spaces, basis, continuity, connectedness, compactness
• Selected Topics: Product and quotient topologies, manifolds, normality and extension theorems, the fundamental group, covering spaces