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 is .

Proposition

Suspension is a functor from the category of topological spaces to itself.

Proof A continuous map suspends to , which is the quotient of . Moreover , so is a functor.

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.