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.
- The join of two spaces is homeomorphic to a sum of cartesian products of cones over the spaces and the spaces themselves, where the sum is taken over the cartesian product of the spaces:
- Given basepointed CW complexes (A,a0) and (B,b0), the "reduced join"
is homeomorphic to the reduced suspension
- Hatcher, Allen, Algebraic topology. Cambridge University Press, Cambridge, 2002. xii+544 pp. ISBN 0-521-79160-X and ISBN 0-521-79540-0
- This article incorporates material from Join on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.
- Brown, Ronald, Topology and Groupoids Section 5.7 Joins.