Quiz, week 4

Find a metric space $(X, d)$ in which the set $A = \mathbb{R}_{++}$ is a closed set. (Challenge: what about an open ball?)

Consider the circle $A = \{a ∈ \mathbb{R}² : d₂(a, (0, 0)) = 1\}$. What is the boundary of $A$ inside the metric space $(\mathbb{R}², d₂)$?