1. 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 C H.

(a) {l/k: kEN} U {a}.

(b) {(x, y) E R2 : a ::; x2 + y2 ::; b} for real numbers 0 < a < b.

(c) {(x, y) E R2 : y = sin(l/x) for some x E (0,1]}.

(d) {(x, y) E R2 : Ixyl ::; 1}.