Open set

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.

Open sets are the basic objects in topology, in terms of which all other objects are defined.