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Algebraic Topology: Course Outline (MAT-603)

Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces.

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Course Outline

  • The Tychonoff theorem.
  • One-point compactification.
  • The Stone-Cech compactification. 
  • Paracompactness. 
  • Lindelof spaces.
  • Stone's theorem.
  • Metrizability.
  • The Nagata-Smirnov metrization theorem.
  • Homotopy paths.
  • Fundamental group.
  • Simply-connected spaces. 
  • Retracts and deformation retracts.
  • The fundamental groups of the circle.
  • The punctured plane and the n-sphere.
  • Van Kampen's theorem.

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