# How is set of points distanced $\leq r$ from set $S$ is called

What is name of the notion described below.

Let S be any body (set of points) in Euclidian n-dimensional space.

Let H(S,r) be set of all points x that distance between x and y is <= r for some $y \in S$.

In other words, it is union all of spheres of radius r and centered in S.

What is name of this H(S,r) set. Is it r-Neighborhood of S ?

Thanks

-

$r$-neighborhood is fine. See http://en.wikipedia.org/wiki/Neighbourhood_(mathematics)#In_a_metric_space.
Isn't that normally for the set of points strictly less than $r$? The OP is using $\leq r$. – Grumpy Parsnip Apr 28 '11 at 18:39
@Jim, ok, closed $r$-neighborhood then :-) Thanks for pointing that out anyway. – lhf Apr 28 '11 at 18:44