Some possible topics for presentation.  These should be (ideally) less than a class period.
  
You can work with someone, but then it should be a slightly more ambitious
presentation.

Hahn-Banach Theorem (TAKEN)

Lyapunov's Theorem  (proof or applications)

Krein-Milman Theorem (proof or applications)

Hilbert Basis Theorem (proof)

Fractals (at least one person has expressed an interest in this, but more can work on it)
  (A couple of possible topics here:
   a. Hausdorff measure/dimension of fractals
   b. Generation, eg as fixed points of contraction functions, 
      or from iterated function systems
   c. Chaos/attractors
   d. Something else?)

Gromov metric
  (Definition, and proof of precompactness)

Haar measure
  (sketch of existence proof)

Ergodic Theorem
  (Statement and proof - I have a reference with a simple proof of a strong form)

Ultrafilters
  (A couple of possible topics here, for example
   a. Existence of ultrafilter
   b. Applications, eg limits via ultrafilters; Tychonoff; uktraproduct)


Something Else?  (I'll add to this list, or you can make a suggestion)