Suspension
Suspension
The suspension of a topological space
is the quotient of obtained by collapsing to a point and to a point. The suspension is denoted by or .
e.g. Suspension of
Proposition
Suspension is a functor from the category of topological spaces to itself.
Proof A continuous map
Wedge Sum
Wedge Sum
The wedge sum of a family of pointed spaces
is the quotient of the disjoint union obtained by identifying all the base points to a single point. The wedge sum is denoted by .
Join
Join
The join of two spaces
and is the union of all line segments joining points of to points of . This is a quotient.