Space (mathematics) - Revision history

Karl Jones at 04:28, 4 September 2016

2016-09-04T04:28:20Z

Karl Jones: /* Description */

2016-09-04T04:17:27Z

‎Description

Karl Jones at 03:54, 4 September 2016

2016-09-04T03:54:21Z

Karl Jones: /* See also */

2016-09-04T03:45:01Z

‎See also

Karl Jones: /* See also */

2016-04-04T23:53:09Z

‎See also

Karl Jones: /* External links */

2016-04-04T21:53:31Z

‎External links

Karl Jones: /* See also */

2016-04-04T21:53:14Z

‎See also

Karl Jones: /* See also */

2016-04-04T21:52:40Z

‎See also

Karl Jones: Created page with "In mathematics, a '''space''' is a set (sometimes called a universe) with some added structure...."

2016-04-04T21:39:14Z

Created page with "In mathematics, a '''space''' is a set (sometimes called a universe) with some added structure...."

New page

In [[mathematics]], a '''space''' is a [[Set (mathematics)|set]] (sometimes called a [[Universe (mathematics)|universe]]) with some added [[Mathematical structure|structure]].

== Description ==

Mathematical spaces often form a hierarchy, i.e., one space may inherit all the characteristics of a parent space.

For instance, all inner product spaces are also normed vector spaces, because the inner product induces a norm on the inner product space.

== See also ==

* [[Mathematics]]
* [[Set (mathematics)]]
* [[Structure]]
* [[Universe (mathematics)]]

== External links ==

* [https://en.wikipedia.org/wiki/Space_(mathematics) Space (mathematics)] @ Wikipedia

[[Category:Mathematics]]
[[Category:Structure]]

@@ Line 15: / Line 15: @@
 Such a definition "from scratch" is now not often used, since it does not reveal the relation of this space to other spaces.
-The modern approach defines the three-dimensional Euclidean space more algebraically, via [[Vector space|vector spaces]] and [[Quadractic form|quadratic forms]], namely, as an affine space whose difference space is a three-dimensional inner product space.
+The modern approach defines the three-dimensional Euclidean space more algebraically, via [[Vector space|vector spaces]] and [[Quadratic form|quadratic forms]], namely, as an affine space whose difference space is a three-dimensional inner product space.
 == See also ==
@@ Line 44: / Line 44: @@
 * [[Polish space]]
 * [[Probability space]]
 * [[Quotient space]]
 * [[Set (mathematics)]]

← Older revision		Revision as of 03:54, 4 September 2016
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−	In [[mathematics]], a '''space''' is a [[Set (mathematics)\|set]] (sometimes called a [[Universe (mathematics)\|universe]]) with some added [[Mathematical structure\|structure]].	+	[[File:Mathematical_Spaces.svg\|250px\|thumb\|A hierarchy of mathematical spaces: The inner product induces a norm. The norm induces a metric. The metric induces a topology.]]In [[mathematics]], a '''space''' is a [[Set (mathematics)\|set]] (sometimes called a [[Universe (mathematics)\|universe]]) with some added [[Mathematical structure\|structure]].

	== Description ==		== Description ==

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 * [[Minkowski space]]
 * [[Normed vector space]]
 * [[Polish space]]
 * [[Probability space]]

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 * [[Normed vector space]]
 * [[Polish space]]
 * [[Quotient space]]
 * [[Set (mathematics)]]

← Older revision		Revision as of 21:53, 4 April 2016
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	[[Category:Mathematics]]		[[Category:Mathematics]]
		+	[[Category:Set theory]]
	[[Category:Structure]]		[[Category:Structure]]

@@ Line 5: / Line 5: @@
 Mathematical spaces often form a hierarchy, i.e., one space may inherit all the characteristics of a parent space.
 For instance, all inner product spaces are also normed vector spaces, because the inner product induces a norm on the inner product space.
 == See also ==

@@ Line 34: / Line 34: @@
 * [[Quotient space]]
 * [[Set (mathematics)]]
 * [[Transport of structure]]
 * [[Sobolev space]]

@@ Line 9: / Line 9: @@
 == See also ==
 * [[Mathematics]]
 * [[Set (mathematics)]]
-* [[Structure]]
+* [[Transport of structure]]
 * [[Universe (mathematics)]]
 == External links ==