Cone space: Difference between revisions

Revision as of 23:23, 2 November 2007

Definition

Given a topological space $X$ , the cone space of $X$ , denoted as $C X$ , is defined as the quotient of $X \times I$ by the equivalence relation:

$(x_{1}, 0) \sim (x_{2}, 0) \forall x_{1}, x_{2} \in X$

Refer:

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

@@ Line 1: / Line 1: @@
-{{self-functor on topospaces}}
 ==Definition==
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 <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