1999/07/16 by J. E. Keesling, James Keesling, Keesling, J. E. +2
Engineering · Mathematics · #28A78 54E40 (Primary) 54H15 (Secondary) #Artificial Immune Systems Applications #Dynamical Systems (math.DS) #FOS: Mathematics #General Topology (math.GN) #Mathematical Dynamics and Fractals #math.DS #math.GN #msc:28A78 #msc:54E40 #msc:54H15
paper · pdf · doi:10.48550/arxiv.math/9907111
14 pages
arxiv created 1999/07/16 · openalex publication_date 1999/07/16 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define the similarity boundary of a self-similar set and use it to analyze the properties of self-similar sets in the general setting of any complete metric space. The similarity boundary is an attempt at extending the concept of the topological boundary in a way that is consistent with our intuitive understanding of the term boundary. We also show how with the analysis of the similarity boundary, we can restrict ourselves to the space K and disregard the ambient space.