Exam I will be in the usual classroom at 7:00 p. m. on Tuesday, September 28, 2004. The exam is closed-book and closed-notes; that is, all you will need is something with which to write. You will have up to 2 hours to work.

Try to give clear, concise responses to the questions. You can and should make use of standard results when they can be applied, such as the Basis Recognition Theorem, or the fact that x is in the closure of A if and only if every neighborhood of x meets A. It may be helpful to include pictures and diagrams in some of your arguments; of course, a picture does not replace an argument, it just makes it easier for the reader to understand.

For problems with the instruction ``Prove or give a counterexample'', one should give a proof is the statement is true, and give an explicit counterexample if it is false.

The following three topics will be especially important: the Hausdorff property, the subspace topology, basis.

There will not be much on isometries and affine transformations of the plane.

The following topics will not appear on the exam:

1.	epsilon-delta definition of continuity
2.	piecing together to obtain continuous functions
3.	locally finite collections of sets
4.	barycentric coordinates
5.	piecewise-linear homeomorphisms of the plane
6.	group theoretic concepts such as conjugacy classes, cosets, normal subgroups, etc.