MATH 560 Introduction to Topology

• What is Topology?
• More on What is Topology?
• Course Details
• Outline
• Syllabus
• Grading
• Help Sessions

Lectures

• Section 1.2 Sets
• Section 1.3 Extended Set Operations
• Section 1.4 Functions
• Section 1.5 Images and Inverse Images of Sets
• Section 2.1 Open Subsets of the Real Numbers
• Section 2.2 Topological Spaces
• Section 2.3 Closed Sets and Closure
• Section 2.4 Limit Points, Interior, Boundary, and Exterior
• Section 2.5 Basic Open Sets
• Section 3.1 Subspaces
• Section 3.2 Continuity
• Section 3.3 Homeomorphisms
• Section 3.4 The Topology of Rⁿ
• Section 3.5 Deformations
• Section 4.1 Products of Two Topological Spaces
• Section 4.2 Products of a Finite Number of Spaces
• Section 4.3 Products of an Infinite Number of Spaces
• Section 4.4 Continuity of the Algebraic Operations on R
• Section 5.1 Connected Spaces
• Section 5.2 Properties of Connected Spaces
• Section 5.3 Products of Connected Spaces
• Section 6.1 Compact Spaces
• Section 6.2 Properties of Compact Spaces
• Section 6.3 Products of Compact Spaces
• Section 8.1 Metric Spaces
• Section 8.2 Properties of Metric Spaces
• Section 8.3 Uniform Continuity
• Section 8.4 The Hausdorff Metric
• Section 8.5 Sequences
• Section 8.6 Complete Metric Spaces
• Section 9.1 Homotopy and the Fundamental Group

Handouts

• Morphing a Ball into a Doughnut and Back
• Mobius Strips and Klein Bottles
• Mobius Strips, Klein Bottles, and More
• Sample Proofs in Set Theory
• Logic and Mathematical Proof
• Implication and Universal Quantifiers