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) \ | <math>(x_1,0) \sim (x_2,0)</math> | ||
and | and | ||
<math>(x_1,1) \ | <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.