Identify which of the following sets are compact and which are not. If E is not compact, find the smallest compact set H (if there is one) such that E ⊂ H.
a) [1/k : k ∈ N} U {0}
b) {(x, y) ∈ R2 : a < x2 + y2 < b) for real numbers 0 < a < b
c) {(x, y) ∈ R2 : y = sin(l/x) for some x ∈ (0, 1]}
d) {x, y) ∈ R2: |xy| < 1}