Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the support of a function is the set of points where the function is not zero, or the closure of that set . This concept is used very widely in mathematical analysis. In the form of functions with support that is bounded, it also plays a major part in various types of mathematical duality theories.A function supported in Y must vanish in X \ Y. For instance, f with domain X is said to have finite support if f(x) = 0 for all but a finite number of x in X. Since any superset of a support is also a support, attention is given to properties of subsets of X that admit at least one support for f. When the support of f (written supp(f)) is mentioned, it may be the intersection of all supports, {x in X: f(x) ≠ 0} (the set-theoretic support), or the smallest support with some property of interest.