University of Galway

Course Module Information

Course Modules

Semester 2 | Credits: 5

An introduction to the theory and application of topology.

Learning Outcomes
  1. Understand and use the basic algebra of set theory, including De Morgan's Laws.
  2. State the definition of a topological space and describe several examples of this concept.
  3. Explain the relationship between topologies and continuous functions.
  4. Understand the concept of homeomorphism.
  5. Construct new topological spaces using the subspace and quotient constructions.
  6. Understand and explain the concept of compactness, prove some basic theorems relating to this concept.
  7. Understand and explain the concept of connectedness, prove some basic theorems relating to this concept.
  8. Apply topological ideas to solve problems in other areas of mathematics or applied mathematics e.g. topological proof of the fundamental theorem of algebra or a proof of the Brouwer fixed point theorem.
Assessments
  • Written Assessment (100%)
Teachers
Reading List
  1. "Introduction to Topology, Pure and Applied" by Adams and Franzosa
    Publisher: Pearson
The above information outlines module MA535: "Topics in Analysis II" and is valid from 2015 onwards.
Note: Module offerings and details may be subject to change.