Learning outcomes

After studying this course, you should be able to:

• explain the terms surface, surface in space, disc-like neighbourhood and half-disc-like neighbourhood

• explain the terms n-fold torus, torus with n holes, Möbius band and Klein bottle

• explain what is meant by the boundary of a surface, and determine the boundary number of a given surface with boundary

• construct certain compact surfaces from a polygon by identifying edges

• explain how a surface in space can be regarded as a topological space.