Math 244 Topology: Point Set

Textbook: 

• Introduction to Topology by Bert Mendelson, 3rd Edition.

Topics:

Chapter 2 Metric Spaces

• Metric spaces

• Continuity

• Open balls and neighborhoods 

• Limits

• Open sets and closed sets

• Subspaces and equivalence of metric spaces

Chapter 3 Topological Spaces

• Topological spaces

• Neighborhoods and neighborhood spaces

• Closure, interior, boundary

• Functions, continuity, homeomorphism

• Subspaces

• Products

Chapter 4 Connectedness

• Connectedness

• Connectedness on the real line

• Path-connected topological spaces

Chapter 5 Compactness

• Compact topological spaces

• Compact subsets of the real line

• Products of compact spaces

• Space-filling curves

Final Presentation: 

Students chose their own topics and each gave a 20-minute presentation followed by a 5-minute Q&A session. Here are the topics that were presented:

• Fixed-point Theorems

• Graph embedding on surfaces

• Introduction to knot theory and applications

• Introduction to homotopy groups

• Path-connected spaces

• Persistent homology and applications 

• Prime decomposition of knots

• Topological quantum numbers