Prove that the following two claims hold for any closed set

Question

Prove that the following two claims hold for any closed set C ⊆ R^m (recall that M is the maximal payoff of the game, in absolute value):

(a) C is approachable by a player if and only if the set {x ∈ C: ? x ? ≤ M} is approachable by the other player.

(b) C is excludable by a player if and only if the set {x ∈ C: ? x ? ≤ M} is excludable by the player.

(c) Show that if C is not closed, item (a) above does not necessarily hold.