Whitney umbrella

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In mathematics, specifically in the field of singularity theory, the Whitney umbrella (also referred to as Whitney's umbrella) is a self-intersecting rectangle placed in three dimensions, given by the implicit equation

x²z − y² = 0.

It is named after the American mathematician Hassler Whitney.

It is closely related to the cross-cap but also includes a handle, a degenerate line of points along the negative z axis.

[edit] References

• Whitney's Umbrella. The Topological Zoo. The Geometry Center. Retrieved on 2006-03-08. (Images and movies of the Whitney umbrella.)