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Should be in both categories.
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)]] 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.
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.
==References==
{{reflist}}
[[Category:Topology]]
[[Category:Topology]]
[[Category:Mathematics]]