Cone space - Revision history

Vipul at 03:00, 25 December 2010

2010-12-25T03:00:11Z

← Older revision		Revision as of 03:00, 25 December 2010
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	==Definition==		==Definition==

	Given a [[topological space]] <math>X</math>, the '''cone space''' of <math>X</math>, denoted as <math>CX</math>, is defined as the quotient of <math>X \times I</math> by the equivalence relation:		Given a [[topological space]] <math>X</math>, the '''cone space''' of <math>X</math>, denoted as <math>CX</math>, is defined as the [[defining ingredient::quotient topology\|quotient]] of <math>X \times I</math> (where <math>I</math> is the [[defining ingredient::closed unit interval]] <math>[0,1]</math> and we use the [[defining ingredient::product topology]]) by the equivalence relation:

	<math>(x_1,0) \sim (x_2,0) \forall x_1,x_2 \in X</math>		<math>(x_1,0) \sim (x_2,0) \forall x_1,x_2 \in X</math>

Vipul at 23:39, 9 October 2010

2010-10-09T23:39:10Z

← Older revision		Revision as of 23:39, 9 October 2010
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	<math>(x_1,0) \sim (x_2,0) \forall x_1,x_2 \in X</math>		<math>(x_1,0) \sim (x_2,0) \forall x_1,x_2 \in X</math>

	Here, <math>I</math> refers to the [[unit interval]].		Here, <math>I</math> refers to the [[closed unit interval]] <math>[0,1]</math>.

	Refer:		Refer:

Vipul at 23:28, 9 October 2010

2010-10-09T23:28:49Z

← Older revision		Revision as of 23:28, 9 October 2010
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	<math>(x_1,0) \sim (x_2,0) \forall x_1,x_2 \in X</math>		<math>(x_1,0) \sim (x_2,0) \forall x_1,x_2 \in X</math>

			Here, <math>I</math> refers to the [[unit interval]].

	Refer:		Refer:

Vipul at 23:28, 9 October 2010

2010-10-09T23:28:26Z

← Older revision		Revision as of 23:28, 9 October 2010
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			{{interval-cum-mapping construct}}

	==Definition==		==Definition==

Vipul: 3 revisions

2008-05-11T19:42:04Z

3 revisions

← Older revision	Revision as of 19:42, 11 May 2008
(No difference)

Vipul at 23:23, 2 November 2007

2007-11-02T23:23:48Z

← Older revision		Revision as of 23:23, 2 November 2007
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	~~{{self-functor on topospaces}}~~

	==Definition==		==Definition==

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	<math>(x_1,0) \sim (x_2,0) \forall x_1,x_2 \in X</math>		<math>(x_1,0) \sim (x_2,0) \forall x_1,x_2 \in X</math>

	~~==Relation with other functors==~~		Refer:

	~~===Related functors===~~

	* [[Suspension]]

	~~==Properties of cone spaces==~~

	~~{{contractible}}~~		* [[Cone space functor]] to see the properties of the cone space functor
			* [[Cone-realizable space]] to see the property of a topological space being realizable as the cone space over some space

Vipul at 22:00, 26 September 2007

2007-09-26T22:00:51Z

← Older revision		Revision as of 22:00, 26 September 2007
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	* [[Suspension]]		* [[Suspension]]

			==Properties of cone spaces==

			{{contractible}}

Vipul at 13:44, 22 May 2007

2007-05-22T13:44:39Z

New page

{{self-functor on topospaces}}

==Definition==

Given a [[topological space]] <math>X</math>, the '''cone space''' of <math>X</math>, denoted as <math>CX</math>, is defined as the quotient of <math>X \times I</math> by the equivalence relation:

<math>(x_1,0) \sim (x_2,0) \forall x_1,x_2 \in X</math>

==Relation with other functors==

===Related functors===

* [[Suspension]]