For each of the sets in the metric space R d1 state whether

For each of the sets in the metric space (R, d_1) state whether the set is closed, bounded, compact (support your answer with a short sentence or two): (- infinity, 1) (1, infinity), (1,2) (3) (1,2).

Solution

(a) The set is neither closed nor compact is unbounded .

(b) The set is neither closed nor compact and unbounded

(c) The set is not closed as isolated points form open sets hence not compact . The set is also not bounded