Homework for Week 3

Part 1

1. Prove that any single point in Aⁿ is a variety. What is its ideal?
2. Prove that any finite set of points in Aⁿ is a variety. What is its ideal?

Part 2

1. List all possible topologies on {0,1} (by, for instance, writing their open sets).
2. For each pair of the topologies in the previous problem, list all possible continuous functions f: {0,1} → {0,1}.

• Part 1: Due Tuesday
• Part 2: Due Thursday