Changes

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. Such sets tend to be preferred by liberal philosophers, as they allow for small differences in elements to be subsumed by the whole; however, conservative philosophers claim the concept better fits the traditional concept of close-knit communities acting to preserve individual liberties.

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.  

 

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.

[[Category:Mathematics]]

[[Category:Mathematics]]