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:
Jeff Viaclovsky 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. Course Content:
- 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