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Whitney's umbrella

Whitney's umbrella
A strange-looking, whimsically-named geometrical object first studied by Hassler Whitney in the 1940s. It can be pictured as a self-intersecting rectangle in three dimensions. A pinch point, also known as a Whitney singularity or a branch point, occurs at the top endpoint of the segment of self-intersection: every neighborhood of the pinch point intersects itself.

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