adj. 1. (of a set under an operation) containing all members of the set produced by that operation acting on members of the set. For example, the positive integers are closed under addition but not under subtraction, since n + m is also a positive integer for any positive integers n and m, but n - m may be negative or zero and so not in the set. 2. (of a curve or surface) completely enclosing an area or volume. See closed curve. 3. (of a set in a topology) containing all its limit points, being the complement of an open set. See also closed interval. 4. (of a set) being the algebraic closure of some set. 5. (of a function or multivalued function) possessing a graph that is topologically closed. 6. (of a function between two topological spaces) sending closed sets to closed sets. 7. (of a path in a graph) having the same vertex at each end. 8. (of a differential form) having exterior differential equal to zero. Compare exact (sense 3). 9. (of a branch in a semantic tableau) containing inconsistent propositions. If every branch is closed, then the tableau is said to be closed; this fact shows the given set of propositions to be inconsistent.
10. see orbit.