Closed set
In topology, a closed set is one which contains all of its limit points. Equivalently, a set in some topological space (including, for example, any metric space) is closed if and only its complement is an open set, or alternatively if its closure is equal to itself.
One common example of a closed set is a closed interval ![$[a, b] = \{x \mid a \leq x \leq b\}$](http://latex.artofproblemsolving.com/1/3/9/13960dbd81a2bcac0fa24c031283321ec49b7365.png)
of the real numbers. However, closed subsets of 
can take a variety of more complicated forms. For example, the set 
is closed, as is the Cantor set.
This article is a stub. Help us out by expanding it.
