closed
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.
closed
The set of integers is closed under the usual arithmetic operations of addition, subtraction, and multiplication, but is not closed under division.