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