# 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).