Reduced suspension

From Topospaces
Jump to: navigation, search

Template:Self-functor on topospaces

Definition

Given a topological space with basepoint (X,x_0), the reduced suspension of X is defined in the following equivalent ways:

(x_0,t) \sim (x_0,t')

The reduced suspension of X is denoted by \Sigma X.

Facts

The reduced suspension commutes with joins. In other words:

\Sigma(X * Y) = \Sigma X * \Sigma Y