MAT 562 Elementary Topology

Spring 2016

Exams

• Exam 1
• Exam 2
• Final Exam

Homework

• 1: Review of sets and related topics
• 2.1: Notion of a metric space
• 2.2: Neighborhoods
• 2.3: Open Sets
• 2.4: Closed Sets
• 2.5: Convergence of sequences
• 2.6: Continuity
• 2.7: Distance between sets
• 3.1: The notion of a topology
• 3.2: Bases and subbases
• 3.3: Open Neighborhood Systems
• 3.4: Finer and coarser topologies
• 3.5: Derived sets
• 3.6: More on derived sets
• 4.1-2: Subspaces, derived sets in them
• 4.3: Continuity
• 4.4: Homeomorphisms}
• 4.6: Product spaces
• 5.2: Hausdorff (T₂) spaces
• 5.3: Regular spaces
• 5.4: Normal spaces
• 5.5a: Continuous extension of functions 1
• 5.5b: Continuous extension of functions 2
• 7.1-2: Open covers and countability
• 7.3: Compactness
• 7.4: Compactness and derived spaces
• 8.1: Compactness in Rⁿ and metric spaces
• 8.2: Local compactness
• 9.1-2: Connectedness, path-connectedness
• 9.3: Connectedness of derived sets
• 9.4: Components; local connectedness