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Metric Spaces (Advanced)

MATH3961

Topology, developed at the end of the 19th Century to investigate the subtle interaction of analysis and geometry, is now one of the basic disciplines of mathematics. A working knowledge of the language and concepts of topology is essential in fields as diverse as algebraic number theory and non-linear analysis. This unit develops the basic ideas of topology using the example of metric spaces to illustrate and motivate the general theory. Topics covered include: Metric spaces, convergence, completeness and the contraction mapping theorem; Metric topology, open and closed subsets; Topological spaces, subspaces, product spaces; Continuous mappings and homeomorphisms; Compact spaces; Connected spaces; Hausdorff spaces and normal spaces, Applications include the implicit function theorem, chaotic dynamical systems and an introduction to Hilbert spaces and abstract Fourier series.

Unit of study details

Unit of study level: Senior

Credit points: 6

Commencing semesters: 1

Further unit of study information

Unit of study handbook: MATH3961

Costs and scholarships information: Costs and Scholarships

Final dates to withdraw from units of study: Census Dates

Available for study abroad and exchange: Yes

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