Differential Geometry
In differential geometry, zero sets are frequently used to define manifolds. An important spacial case is the case that f is a smooth function from Rp to Rn. If zero is a regular value of f then the zero-set of f is a smooth manifold of dimension m=p-n by the regular value theorem.
For example, the unit m-sphere in Rm+1 is the zero set of the real-valued function f(x) = |x|2 - 1.
Read more about this topic: Zero Set
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