Join (topology)
In topology, a field of mathematics, the join of two topological spaces A and B, often denoted by or, is defined to be the quotient space
where I is the interval and R is the equivalence relation generated by
At the endpoints, this collapses to and to.
Intuitively, is formed by taking the disjoint union of the two spaces and attaching line segments joining every point in A to every point in B.Examples
is homeomorphic to the reduced suspension
of the smash product. Consequently, since is contractible, there is a homotopy equivalence
