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, Department of Mathematical and Computer Sciences, Metropolitan State University of Denver
Curtis, Bryan A.
"Reversing A Doodle,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 17
, Article 5.
Available at: http://scholar.rose-hulman.edu/rhumj/vol17/iss1/5