1. Mark each statement True or False. Justify each answer.
(a) If x, y ∈ (X, d ) and d (x, y) = 0, then x = y.
(b) If x, y ∈ (X, d ) and d (x, y) > 0, then x ≠ y.
(c) If x, y ∈ (X, d ), then d (x, y) = d ( y, x).
(d) If x, y, z ∈ (X, d ), then d (x, y) = d (x, z) + d(z, y).
2. Mark each statement True or False. Justify each answer.
(a) If S is a nonempty open proper subset of a metric space X, then X \S is not open.
(b) If S is a compact subset of a metric space X, then S is closed and bounded.
(c) If S is a closed bounded subset of a metric space X, then S is compact.
(d) If S is a compact subset of a metric space X, then S has an accumulation point in S.