High Quality Content by WIKIPEDIA articles! In mathematics, the zero set of a real-valued function f : X ? R (or more generally, a function taking values in some additive group) is the subset f ? 1(0) of X (the inverse image of 0). In other words, the zero set of the function f is the subset of X on which f(x) = 0. The cozero set of f is the complement of the zero set of f (i.e. the subset of X on which f is nonzero). Zero sets are important in several branches of geometry and topology. 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.

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