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Surfaces are a special class of topological spaces that crop up in many places in the world of mathematics. In this free course, you will learn to classify surfaces and will be introduced to such concepts as homeomorphism, orientability, the Euler characteristic and the classification theorem of compact surfaces.
Course 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.
First Published: 10/08/2012
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- Learning outcomes
- 1 Topological spaces and homeomorphism
- 2 Examples of surfaces
- 2 Examples of surfaces
- 2.1 Surfaces in space
- 2.2 Surfaces in space
- 2.3 Paper-and-glue constructions
- 2.4 Homeomorphic surfaces
- 2.5 Defining surfaces
- 3 The orientability of surfaces
- 4 The Euler characteristic
- 5 Edge identifications
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About this free course
20 hours study
Level 3: Advanced
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