
The exam will cover a subset of the following topics:
basis (and how to generate a topology from a basis)
subspace topology
Hausdorff spaces
closed subsets
standard topology (on R^n)
discrete topology
dictionary order topology
finitecomplement topology
product topology
box topology
metric spaces
continuity (definition, examples, properties)
connectedness (definition, examples, properties)
compactness (definition, examples, properties)
the intermediate value theorem
the extreme value theorem
the supremum (on R)
surfaces (examples, basic properties; these show up on at most 5% of the exam)
manifolds (definitions, examples, nonexamples; these show up on at most 5% of the exam)
As usual, you are free to use any result from the textbook or lecture, provided you are not being asked to prove exactly that result (or a very slight modification of it). If you are unsure during the exam, just ask.
To study, I suggest you look at the following (in descending order of importance): the study guide, the homework assignments (including suggested problems), proofs of theorems from class, previous tests and their study guides.
My usual office hours are no longer applicable, now that classes are over. However, I will be holding extra office hours on April 17 and April 24 from 12 to 2.
Midterm Test 1: Friday, February 9 from 2:30 to 3:20 in ABB 136;
Midterm Test 2: Friday, March 16 from 2:30 to 3:20 in ABB 136.