Open set - Revision history

SamHB: Should be in both categories.

2016-04-17T02:37:18Z

Should be in both categories.

2010-02-07T19:55:13Z

2008-08-31T18:17:43Z

masking link, reference, and def of ball in its own article now

2008-08-31T01:44:34Z

too much jargon - it better not be deliberate

2008-08-31T01:44:01Z

arcane and esoteric - give us basic math, or stop making articles like this

2008-08-31T01:43:16Z

How is a ball different from a solid sphere, and how is this relevant?

2008-08-31T01:42:22Z

2008-08-31T00:39:29Z

need source and links to more basic concepts

2008-08-30T23:53:33Z

de-vague-ing with explanation

2008-08-30T23:44:38Z

Explain what you mean by a "ball"

@@ Line 1: / Line 1: @@
-{{jargon}}
+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.
 Open sets are the basic objects in [[topology]], in terms of which all other objects are defined.

@@ Line 1: / Line 1: @@
 {{jargon}}
-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)|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.
 Open sets are the basic objects in [[topology]], in terms of which all other objects are defined.
 [[Category:Topology]]

← Older revision		Revision as of 01:44, August 31, 2008
Line 1:		Line 1:
−	{{~~esoteric~~}}	+	{{jargon}}
	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.

← Older revision		Revision as of 01:44, August 31, 2008
Line 1:		Line 1:
−	{{~~arcane~~}}	+	{{esoteric}}
	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.

← Older revision		Revision as of 01:43, August 31, 2008
Line 1:		Line 1:
		+	{{arcane}}
	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.

← Older revision		Revision as of 23:44, August 30, 2008
Line 1:		Line 1:
		+	{{vague}}
	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.		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.