Algebraic Topology: Course Outline (MAT-603)

• 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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