Final Exam Topics

Chapter 1

• Open and closed sets
• Limit points of a set
• Characterization of closed sets
• Sequences and convergence. Relation with limit points
• Subset topology
• Definition of topology
• Examples of topologies
• Equivalence relations
• Quotient spaces
• Hausdorff spaces
• Continuous functions
• Homemorphisms
• Topological properties
• Path-connectedness
• Connectedness
• Compactness in Rⁿ

Chapter 2

• Definition of manifold
• Definition of surface
• Definition of surface with boundary
• Connected sum construction
• Plane models of surfaces
• Orientability
• Classification of surfaces

Chapter 1

• Cell complexes
• Euler characteristic
• Genus
• Regular complexes
• Platonic solids - duality

Chapter 4

• Maps and map coloring
• Heawood number
• Statement of the four color problem