From Wikipedia, the free encyclopedia
At the endpoints, this collapses to and to .
Intuitively, is formed by taking the disjoint union of the two spaces and attaching a line segment joining every point in A to every point in B.
- The join is homeomorphic to sum of cartesian products of cones over spaces and spaces itself, where sum is taken over cartesian product of spaces:
- The join of subsets of n-dimensional Euclidean space A and B is homotopy equivalent to the space of paths in n-dimensional Euclidean space, beginning in A and ending in B.
- The join of a space X with a one-point space is called the cone CX of X.
- The join of a space X with (the 0-dimensional sphere, or, the discrete space with two points) is called the suspension of X.
- The join of the spheres and is the sphere .
- 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.