# Open Set

An open set is a set for which every point in the set has a neighborhood lying in the set. An open set is the complement of a closed set and. An open interval is an example of an open set.

Open set is a college-level concept that would be first encountered in a topology course covering point-set topology.

### Examples

Interval: | An interval is a connected piece of the real number line which may be open or closed at either end. |

### Prerequisites

Neighborhood: | The neighborhood of a point is an open set containing that point. |

Set: | In mathematics, a set is a finite or infinite collection of objects in which order has no significance and multiplicity is generally also ignored. |

Topological Space: | A topological space is a set with a collection of subsets T that together satisfy a certain set of axioms defining the topology of that set. |