2019/08/20 by Flesch, János, Predtetchinski, Arkadi, Suomala, Ville
#51F99 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #General Topology (math.GN) #Metric Geometry (math.MG) #Primary 54E35 #Secondary 28A12
paper · doi:10.48550/arxiv.1908.07566
We introduce the so--called doubling metric on the collection of non--empty bounded open subsets of a metric space. Given a subset U of a metric space X, the predecessor U* of U is defined by doubling the radii of all open balls contained inside U, and taking their union. If U is open, the predecessor of U is an open set containing U. The directed doubling distance between U and another subset V is the number of times that the predecessor operation needs to be applied to U to obtain a set that contains V. Finally, the doubling distance between U and V is the maximum of the directed distance between U and V and the directed distance between V and U.