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.

Author Bio

As an undergraduate student at Metropolitan State University of Denver, Bryan Curtis worked closely with his adviser Dr. Diane Davis. Under her guidance, Bryan completed many independent studies. One such study resulted in a talk at the 2015 Join Mathematics Meetings and eventually, this paper. Bryan is now pursuing his PhD in mathematics at the University of Wyoming. If you have any questions or comments about this paper, please feel free to contact Bryan.