Editing Closed set (section)

== Examples ==
* The closed [[Interval (mathematics)|interval]] <math>[a, b]</math> of [[real number]]s is closed. (See {{em|[[Interval (mathematics)]]}} for an explanation of the bracket and parenthesis set notation.)
* The [[unit interval]] <math>[0, 1]</math> is closed in the metric space of real numbers, and the set <math>[0, 1] \cap \Q</math> of [[rational number]]s between <math>0</math> and <math>1</math> (inclusive) is closed in the space of rational numbers, but <math>[0, 1] \cap \Q</math> is not closed in the real numbers.
* Some sets are neither open nor closed, for instance the half-open [[Interval (mathematics)|interval]] <math>[0, 1)</math> in the real numbers.
* The [[Line (geometry)#Ray|ray]] <math>[1, +\infty)</math> is closed.
* The [[Cantor set]] is an unusual closed set in the sense that it consists entirely of boundary points and is nowhere dense.
* Singleton points (and thus finite sets) are closed in [[T1 space|T<sub>1</sub> spaces]] and [[Hausdorff spaces]].
* The set of [[integers]] <math>\Z</math> is an infinite and unbounded closed set in the real numbers.
* If <math>f : X \to Y</math> is a function between topological spaces then <math>f</math> is continuous if and only if preimages of closed sets in <math>Y</math> are closed in <math>X.</math>