Single-Valued Function

A single-valued function is function that, for each point in the domain, has a unique value in the range. It is therefore one-to-one or many-to-one.

A single-valued complex function of a complex variable is a complex function f:C->C that has the same value at every point z_0 independent of the path along which it is reached by analytic continuation (Knopp 1996).

See also

Analytic Continuation, Many-to-One, Meromorphic Function, Multiple-Valued Function, One-to-One

Explore with Wolfram|Alpha

References

Knopp, K. Theory of Functions Parts I and II, Two Volumes Bound as One. New York: Dover, Part I p. 103 and Part II p. 93, 1996.

Referenced on Wolfram|Alpha

Single-Valued Function

Cite this as:

Weisstein, Eric W. "Single-Valued Function." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Single-ValuedFunction.html

Subject classifications