Calculate the limit of an=d∞(fn,fn+1)a_n = d_∞(f_n, f_{n+1}), where fn(x)=x/nf_n(x) = x/n and fn:[0,1]→ℝf_n : [0, 1] → \mathbb{R}.
Find a metric space (X,d)(X, d) in which A=ℝ++A = \mathbb{R}_{++} is a closed set. (Challenge: what about an open ball instead?)
Consider the circle A={a∈ℝ²:d₂(a,0)=1}A = \{a ∈ \mathbb{R}² : d₂(a, 0) = 1\}. What is ∂A∂A?