Introductory description

Topology is the study of properties of spaces invariant under continuous deformation. For this reason it is often called ``rubber-sheet geometry''. The module covers: topological spaces and basic examples; compactness; connectedness and path-connectedness; identification topology; Cartesian products; homotopy and the fundamental group; winding numbers and applications; an outline of the classification of surfaces.

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

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Learning outcomes

By the end of the module, students should be able to:

• To explain how to distinguish spaces by means of simple topological invariants (compactness, connectedness and the fundamental group)
• To explain how to construct spaces by gluing and to prove that in certain cases that the result is homeomorphic to a standard space
• To construct simple examples of spaces with given properties (eg compact but not connected or connected but not path connected).

Indicative reading list

Books:
Chapter 1 of Allen Hatcher's book Algebraic Topology
MA Armstrong Basic Topology Springer (recommended but not essential).

Subject specific skills

See learning outcomes.

Transferable skills

Students will acquire key reasoning and problem solving skills which will empower them to address new problems with confidence.