closed_set m21k In topology and related branches of mathematics, a set is called closed if its complement is open. This implies that a closed set contains its own boundary. Intuitively, if you are outside the set, and you "wiggle" a little bit, you will still be outside the set. Note that this notion depends on the concept of "outside", the surrounding space with respect to which the complement is taken. For instance, the unit interval [0,1] is closed in the real numbers, and the set [0,1] ¿ Q of rational numbers between 0 and 1 (inclusive) is closed in the space of rational numbers, but [0,1] ¿ Q is not closed in the real numbers. Some sets are neither open nor closed, for instance the half-open interval [0,1) in the real numbers. 041009 ... . For instance, the unit interval [0,1] is closed in the real numbers, and the set [0,1] ^ Q of rational numbers between 0 and 1 (inclusive) is closed in the space of rational numbers, but [0,1] v Q is not closed in the real numbers. Some sets are neither open nor closed, for instance the half-open interval [0,1) in the real numbers. 041009 what's it to you? who go blather from