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. 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. 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 20:35, August 26, 2008
An open set in Euclidean space is a set that contains a ball around each of its points. 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.