Difference between revisions of "Open set"
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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. | 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. | ||
Revision as of 01:44, August 31, 2008
This article or section needs to be written in plain English, using plain English that most of our readers can understand. Articles that depend excessively on technical terms accessible only to specialists are useless for our purposes, so writers are admonished to avoid jargon
An open set in Euclidean space is a set that contains a ball (mathematics) around each of its points.[Citation Needed] 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.
Open sets are the basic objects in topology, in terms of which all other objects are defined.