A function has compact support if it is zero outside of a compact set. Alternatively, one can say that a function has compact support if its support is a compact set.
For example, the function 
in its entire domain (i.e., 
) does not have compact support, while any bump
function does have compact support.
Compact Support
See also
Bump Function, Compact Set, Global Support, SupportPortions of this entry contributed by Todd Rowland
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Cite this as:
Rowland, Todd and Weisstein, Eric W. "Compact Support." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CompactSupport.html