# Difference between revisions of "Open set"

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− | An '''open set''' in [[Euclidean space]] is a set that contains a ball around each of its points. In Euclidean space, a "ball" of radius ''r'' centered at a point ''p'' is the set of all points which are distance at most ''r'' from ''p''. Intuitively, if a point is contained in an open set, then all points sufficiently close to it are also contained. | + | An '''open set''' in [[Euclidean space]] is a [[set]] that contains a [[ball]] around each of its points.{{fact}} In Euclidean space, a "ball" of radius ''r'' centered at a point ''p'' is the set of all points which are distance at most ''r'' from ''p''. Intuitively, if a point is contained in an open set, then all points sufficiently close to it are also contained. |

Open sets are the basic objects in [[topology]], in terms of which all other objects are defined. | Open sets are the basic objects in [[topology]], in terms of which all other objects are defined. | ||

[[Category:Topology]] | [[Category:Topology]] |

## Revision as of 18:39, 30 August 2008

An **open set** in Euclidean space is a set that contains a ball around each of its points.^{[Citation Needed]} In Euclidean space, a "ball" of radius *r* centered at a point *p* is the set of all points which are distance at most *r* from *p*. Intuitively, if a point is contained in an open set, then all points sufficiently close to it are also contained.

Open sets are the basic objects in topology, in terms of which all other objects are defined.