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This unit is concerned with a special class of topological spaces called surfaces. Common examples of surfaces are the sphere and the cylinder; less common, though probably still familiar, are the torus and the Möbius band. Other surfaces, such as the projective plane and the Klein bottle, may be unfamiliar, but they crop up in many places in mathematics. Our aim is to classify surfaces – that is, to produce criteria that allow us to determine whether two given surfaces are homeomorphic.

This unit is from our archive and is an adapted extract from Topology (M338) which is no longer taught by The Open University. If you want to study formally with us, you may wish to explore other courses we offer in this subject area [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] .