closed / klōzd/ • adj. not open. ∎ (of a business) having ceased trading, esp. for a short period: he put the “Closed” sign up on the door. ∎ no longer under discussion or investigation; concluded: closed cases of alleged contract irregularities. ∎ (of a society or system) not communicating with or influenced by others; independent. ∎ limited to certain people; not open or available to all: the UN Security Council met in closed session. ∎ unwilling to accept new ideas: you're facing the situation with a closed mind. ∎ Math. (of a set) having the property that the result of a specified operation on any element of the set is itself a member of the set. ∎ Math. (of a set) containing all its limit points. ∎ Geom. of or pertaining to a curve whose ends are joined.PHRASES: behind closed doors taking place secretly.closed book a subject or person about which one knows nothing.
The set of integers is closed under the usual arithmetic operations of addition, subtraction, and multiplication, but is not closed under division.