Compact support of a function means that its support is a compact set. On a domain
that is a T2-space, equivalently,
the function is zero outside
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, Support, Test FunctionPortions of this entry contributed by Todd Rowland
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Cite this as:
Weisstein, Eric W., with contributions by Todd Rowland. "Compact Support." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CompactSupport.html