From the closed support section, we see that between at -1 or 1 $1-x^2$ is 0, yet we say the support is [-1, 1] and not (-1, 1)? I thought a support was the set of the domain which does not map to 0?

Further it talks to the closure of the set ... why is the set closure not also (-1, 1)?

  • $\begingroup$ This question is ff topic for this site. $\endgroup$ Apr 6 '18 at 23:04

If the domain of f is a topological space, the support of f is instead defined as the smallest closed set containing all points not mapped to zero.

Euclidean space is a topological space. The closure of a set is the union of an open set and the set of all its limit points, that is all points that are arbitrarily close to a point within the open set. (-1,1) is open, while [-1,1] is closed because it includes the two limit points -1 and 1.


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