The goal of this project is to explore either Point-Set Topology itself or its relevance to other areas of Mathematics.

The student will write a short survey article or investigative article on a topic he or she wishes to investigate concerning Point-Set Topology.  A preliminary version of each paper will be reviewed by the instuctor and another student before a final revision is due.  The preliminary version is due November 17th.  Comments from reviewers are due November 29th.  The final version is due December 8th.

The topics may be just about anything including Analysis, Algebra, Geometery, Algebraic Geometry, Differential Equations, Graph Theory, Continuum Theory, Low-Dimensional Topology, Geometric Topology, Number Theory, etc.  Point-Set Topology figures into every area of Mathematics in some way.  Here are a few suggestions.

• The structure of topologies on a finite set (partial orderings, equivalence under homeomorphism, ...)
• Foliations of the plane by lines
• Denjoy foliation of the torus
• Spec(Z), the set of prime ideals of the integers with the Zariski topology
• Manifolds: continuous, differentiable, smooth, complex, hyperbolic, et al. 
• Compactness of the unit ball in the weak-* topology
• Characterization of the unit interval, circle, Cantor set, etc.
• Non-Archimedian metric spaces (e.g. p-adic numbers)
• Topological groups (pp. 145-146)
• Dimension theory (pp. 304-316)
• Continuum theory

You may also care to search/browse through the General Topology section of the ArXiv to get an idea of some current research topics in Point-Set Topology.  

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Reviewing Papers

Give a copy (physical or electronic) of your paper to the classmate whose name immediately follows yours alphabetically.  Stephen, give yours to Phil.
Send me a copy by email.

Bergonio, Philip 
Brown, Angela 
Byrd, Ryan
Hofmann, Sarah
Jiang, Yunjiang    
Johnson, Aja  
Manning, Justin 
Winburn, Stephen 

Edit the paper you receive for content and clarity.  Were there jumps in logic, non-sequiturs, terminology left undefined?  Is the notation cumbersome or useful?  Stylistically, does the paper flow?  Would it be better rearranged?  Was the paper informative?  Make constructive marks and comments that would help improve the paper.  Give an overview your impression of the paper.

Comments are due Tuesday, November 29th.