Suspension: Difference between revisions

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Given a topological space <math>X</math>, the suspension of <math>X</math>, denoted <math>SX</math>, is defined as the quotient of <math>X \times I</math> by the following two equivalence relations:
Given a topological space <math>X</math>, the suspension of <math>X</math>, denoted <math>SX</math>, is defined as the quotient of <math>X \times I</math> by the following two equivalence relations:


<math>(x_1,0) \simeq (x_2,0)</math>
<math>(x_1,0) \sim (x_2,0)</math>


and
and


<math>(x_1,1) \simeq (x_2,1)</math>
<math>(x_1,1) \sim (x_2,1)</math>


In other words, both ends of the cylinder are shrunk to a point.
In other words, both ends of the cylinder are shrunk to a point.

Revision as of 13:42, 22 May 2007

Template:Self-functor on topospaces

Definition

Given a topological space , the suspension of , denoted , is defined as the quotient of by the following two equivalence relations:

and

In other words, both ends of the cylinder are shrunk to a point.