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MA3F1 Content

Content:
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.

Aims:
To introduce and illustrate the main ideas and problems of topology.

Objectives:
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).

Books:
Chapter 1 of Allen Hatcher's book Algebraic Topology

MA Armstrong Basic Topology Springer (recommended but not essential).