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Surfaces are a special class of topological spaces that crop up in many places in the world of mathematics

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Open University UK

April 3, 2023

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Last updated:

April 3, 2023

Duration:

Unlimited Duration

FREE

This course includes:

Unlimited Duration

Badge on Completion

Certificate of completion

Unlimited Duration

Description

Surfaces are a special class of topological spaces that crop up in many places in the world of mathematics

In this  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.

Course Curriculum

  • Surfaces Unlimited

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