Level Set:

The level set of a surface M in the direction z at the height c is the inverse image of c under the height function on M induced by the direction z.

Less formally, it is the intersection of the surface with the plane perpendicular to z at height c. For a closed surface, the level set will generally be a collection of closed curves.

As the height passes a critical level the topology of the level set will change, usually by changing the number of components of the level set.

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8/12/94 dpvc@geom.umn.edu -- The Geometry Center