Information about Exam I for Math 4853-001

Mathematics 4853-001 - Introduction to Topology - Spring 2010

Information about Exam I

Exam I will be in the usual classroom on Wednesday, February 17, 2010. It will cover the material up through the formal definition of a topological space and the initial examples of topological spaces. 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.

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 these topics:

  1. The epsilon-delta definition of continuity--- verification of examples, using it to prove more general facts about continuity
  2. Open balls and sets in Rⁿ, definitions and properties. Formulation of continuity in terms of open sets.
  3. Definition of a topological space and initial examples.

Questions will probably not concern matters mentioned only briefly in the lectures.

1. The epsilon-delta definition of continuity--- verification of examples, using it to prove more general facts about continuity
2. Open balls and sets in Rⁿ, definitions and properties. Formulation of continuity in terms of open sets.
3. Definition of a topological space and initial examples.