In mathematics, the support of a function is the set of points where the function is not zero-valued, 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.
The most common situation occurs when X is a topological space (such as the real line) and f : X→R is a continuous function. In this case, only closed supports of X are…