Closed
There are two meanings of the word "closed".
In topology
In topology, a region is "closed" iff its complement is open, or alternatively iff it contains all its limit points.
Some examples of closed regions are rectangles with boundary and circles with boundary.
We may also call a manifold "closed" iff it has no boundary, yet is compact.
In functions
A set 
is closed under a function 
iff 
(where 
is the number of arguments that accepts - possibly one).
For example, the real numbers are closed under addition.
