一图了解支撑集

支撑集 简称：支集 ，英文：support set，或者supp（）符号

支集：使函数$f（x）$f（x）值不为0的定义域区间

上图是我自己的理解，不对的地方请指点

感觉很多人都在反复的复制维基百科和百度百科的解释，并没有自己通俗理解，
http://blog.sina.com.cn/s/blog_614cba320101bszn.html可以看一下

以下是百科（英文）

Suppose that f : $X → R$X→R is a real-valued function whose domain is an
arbitrary set $X$X. The set-theoretic support of $f$f, written
supp$(f)$(f), is the set of points in $X$X where f is non-zero

The support of $f$f is the smallest subset of $X$X with the property
that f is zero on the subset’s complement. If$ f(x) = 0$ for all but a
finite number of points $x$x in $X$X, then $f$f is said to have finite
support.

If the set $X$X has an additional structure (for example, a topology),
then the support of $f$fis defined in an analogous way as the smallest
subset of $X$X of an appropriate type such that $f$f vanishes in an
appropriate sense on its complement. The notion of support also
extends in a natural way to functions taking values in more general
sets than $R$R and to other objects, such as measures or distributions.

以下是维基百科

compact subsets ：闭区间