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According to http://mathworld.wolfram.com/CompactSupport.html ,

  1. A function has compact support if it is zero outside of a compact set.
  2. Alternatively, one can say that a function has compact support if its support is a compact set.

My question is, which is the common definition of compact support, $1$ or $2$?

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1 Answer 1

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I would say that the former is slightly more simple to parse, in that for the latter, one must recall that the support of a function is the closure of the set of points where the function is non zero when the function is acting on a topological space, rather than just the set of points. The first is also slightly more common in my experience.

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    $\begingroup$ Yeah, I agree. Thanks. So the phrase 'compact support' does not mean the support is compact. That was really confusing to me. $\endgroup$
    – user66314
    Feb 14, 2015 at 14:39
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    $\begingroup$ Yes it does mean the support is compact. Please recall the definition of support: en.wikipedia.org/wiki/Support_%28mathematics%29#Closed_support . Both of your definitions are equivalent. $\endgroup$
    – wonce
    Feb 15, 2015 at 15:44

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