The Similarity Boundary of a Self-Similar Set

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 intui...

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Bibliographic Details
Published inarXiv.org
Main Authors Keesling, J E, Krishnamurthi, C
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 16.07.1999
Subjects
Metric space
Self-similarity
Similarity
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Summary: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.
ISSN:2331-8422