closed

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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.

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closed A term applied to a set S on whose elements a dyadic operation ◦ is defined and that possesses the property that, for every (s,t) in S, the quantity s t is also in S; S is then said to be closed under ◦. A similar definition holds for monadic operations such as ~. A set S is closed under ~ provided that, when s is in S, the quantity ~s is also in S.

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