1. The question is to show whether A is compact in R2 with the standard topology. A = [0,1]x{0} U {1/n, n\in Z+} x [0,1]
3. If I group the [0,1] together, I get [0,1] x {0,1/n, n \in Z+ }, and [0,1] is compact in R because of Heine Borel and {0}U{1/n} is compact since you can show that every...