AS/SC/MATH4080.06

Topology

Topology is one of the pillars of modern mathematics (along with geometry, algebra and analysis); in fact, it can be viewed as a synthesis of geometry and analysis, strongly influenced by algebraic methods. Its study clarifies the nature of concepts learned in analysis and geometry such as proximity, continuity and distance. It studies objects called topological spaces by studying the maps (functions) that they support, and their invariants.

This is a basic course covering such topics as topological spaces, continuity, connectedness, compactness, fixed-point theory, metric spaces, nets, filters, metrization theorems, complete metric spaces, function spaces, fundamental group, and covering spaces.

More advanced topics in topology that this course leads to are point set topology, algebraic topology (homology theory, homotopy theory) and differential topology (manifold theory). Topology has many applications within mathematics, but nowadays it also is used in physics and physical astronomy (e.g. cosmology) as well as in catastrophe theory and physiology, economics and sociology.

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The course can be used to fulfill the Pure Mathematics Honours requirement.

The final grade will be based on a December exam (30%), a final exam (40%) and assignments (30%).