The radius r neighborhood of a set X, denoted Nr(X), is the collection of points within a distance r of X. We discuss some of the properties preserved by the radius r neighborhood in Rn. In particular, we find a collection of sets which have a unique pre-image when mapped under Nr. This problem has interesting ties to convex geometry.
Diane E. Davis
Curtis, Bryan A.
"Reversing A Doodle,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 17:
1, Article 5.
Available at: https://scholar.rose-hulman.edu/rhumj/vol17/iss1/5