Difference between revisions of "Open set"
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| − | + | An '''open set''', in [[Euclidean space|the kind space we're used to]], is a [[set]] such that, 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 (mathematics)|ball]] around each of its points.<ref>http://mathworld.wolfram.com/OpenSet.html</ref> | + | |
| + | Formally, we say that a set is an open set if it contains a [[ball (mathematics)|ball]] around each of its points.<ref>http://mathworld.wolfram.com/OpenSet.html</ref> | ||
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. | ||
Revision as of 19:55, February 7, 2010
An open set, in the kind space we're used to, is a set such that, intuitively, if a point is contained in an open set, then all points sufficiently close to it are also contained.
Formally, we say that a set is an open set if it contains a ball around each of its points.[1]
Open sets are the basic objects in topology, in terms of which all other objects are defined.