1 The unreduced suspension
The space is sometimes called the unreduced, unbased or free suspension of to distinguish it from the reduced suspension described below.
2 The reduced suspension
If is a based topological space, the reduced suspension of often denoted (or when the basepoint needs to be explicit), is defined to be the quotient space Setting the basepoint of to be the equivalence class of the reduced suspension is a functor from the category of based topological spaces into itself.
An important property of this functor is that it is a left adjoint to the functor taking a (based) space to its loop space . In other words, naturally, where stands for continuous maps which preserve basepoints.
The reduced suspension is also known as the based suspension.
|Date of creation||2013-03-22 13:25:37|
|Last modified on||2013-03-22 13:25:37|
|Last modified by||antonio (1116)|