Mathematics
MA342: Topology (5 ECTS)
An introduction to the theory and application of topology.
Taught in Semester(s) 2. Examined in Semester(s) 2.
Workload: 126 hours (24 Lecture hours, 12 Tutorial hours, 90 Self study hours).
Module Learning Outcomes.
On successful completion of this module the learner should be able to:
- Understand and use the basic algebra of set theory, including De Morgan's Laws.
- State the definition of a topological space and describe several examples of this concept.
- Explain the relationship between topologies and continuous functions.
- Understand the concept of homeomorphism.
- Construct new topological spaces using the subspace and quotient constructions.
- Understand and explain the concept of compactness, prove some basic theorems relating to this concept.
- Understand and explain the concept of connectedness, prove some basic theorems relating to this concept.
- 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.
Indicative Content
Syllabus Outline
- The basic algebra of set theory, unions, intersections, complements, De Morgan's Laws.
- Topological spaces - definitions and basic examples.
- Continuity and Homeomorphism.
- New spaces from old. Subspaces, quotient spaces, products.
- Compactness and connectedness.
- Applications: Using topological ideas to solve problems from other areas of mathematics.
Module Resources
- "Introduction to Topology, Pure and Applied" by Adams and Franzosa (Pearson)
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