1. Let ρ: R2 ×R2 →R be given by ρ((x1,y1),(x2,y2)) = |x1
−x2|+|y1 −y2|.
(a) Prove that (R2,ρ) is a metric space.
(b) In (R2,ρ), sketch the open ball with center (0,0) and radius
1. 2. Let {xn} be a sequence in a metric space (X,ρ). Prove that if
xn → a and xn → b for some a,b ∈ X, then a = b.
3. (Optional) Let (C[a,b],ρ) be the metric space discussed in
example 10.6 on page 344...