MA2223 – Annual exam

MA2223 – Annual exam
The exam will consist of 4 questions and you will need to answer 3.
You will not be asked to explicitly state any definitions or theorems.
You will be asked to (a) reproduce some of the proofs we covered in
class and (b) solve problems similar to those assigned for homework.
Completions, uniform continuity and dual spaces are topics that we
covered very briefly, so these topics will not appear on the exam.
Sample exam question
1. Let (X, T ) be a Hausdorff topological space.
(a) Assume that A ⊂ X is compact. Show that A is closed in X.
(b) Show that B = {(x, y) ∈ X × X : y = x} is closed in X × X.
(c) Consider the case X = R. Find the closure, the interior and the
boundary of C = [0, 1) ∪ {2}. You need not justify your answers.