Exam II will be in the usual classroom on Friday, March 26, 2010. It will cover the material starting with the formal definition of a topological space and ending with the concept of sub-basis (but not including the product topology). Questions might include such things as giving important definitions, arguments that were steps in more complicated proofs we did, proofs for examples similar to examples we did in class, giving examples satisfying certain conditions, or variations on homework problems. The current draft has 52 points.

I will be out of town at a math meeting on March 26, but my replacement knows topology and should be able to address any questions that may come up.

As on any exam, it is wise to start with the problems that you feel more confident that you know how to do, before moving on to others.

Blank paper will be provided, so all you will need is something to write with. Please write your solutions on the blank paper (you may have as many sheets as you need, and may put the problems in any order). Please hand in your exam paper along with your solutions.

The following topics are likely to appear, although the exam is not limited to them:

1. Countable and uncountable sets. Know the standard facts about countable and uncountable sets that we examined in class, and be familiar with the two Cantor-style arguments.
2. Bases and sub-bases. Their definitions and the definitions of the topologies that they generate. The Basis Recognition Theorem and its applications.
3. Continuity. Definition and typical examples. Interpreting continuity for different types of topologies.
4. Homeomorphisms. Definitions and examples.

Test questions are unlikely to concern matters mentioned only in passing in the lectures. There are a lot of important definitions in this part of the course, know them well.