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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> 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.