join
Given two topological spaces X and Y, their join, denoted by X⋆Y, is defined to be the quotient space
X⋆Y:= |
where the equivalence relation is generated by
Intuitively, is formed by taking the disjoint union of the two spaces and attaching a line segment joining every point in to every point in
Some examples:
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The join of a space with a one-point space is called the cone of .
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The join of the spheres and is the sphere .
Title | join |
---|---|
Canonical name | Join1 |
Date of creation | 2013-03-22 13:25:40 |
Last modified on | 2013-03-22 13:25:40 |
Owner | mathcam (2727) |
Last modified by | mathcam (2727) |
Numerical id | 7 |
Author | mathcam (2727) |
Entry type | Definition |
Classification | msc 54B99 |
Related topic | Cone |
Related topic | Suspension![]() |
Defines | join |