Hausdorff Stability of Persistence Spaces

  title={Hausdorff Stability of Persistence Spaces},
  author={Andrea Cerri and Claudia Landi},
  journal={Foundations of Computational Mathematics},
  • A. Cerri, C. Landi
  • Published 1 April 2016
  • Mathematics
  • Foundations of Computational Mathematics
Multidimensional persistence modules do not admit a concise representation analogous to that provided by persistence diagrams for real-valued functions. However, there is no obstruction for multidimensional persistent Betti numbers to admit one. Therefore, it is reasonable to look for a generalization of persistence diagrams concerning those properties that are related only to persistent Betti numbers. In this paper, the persistence space of a vector-valued continuous function is introduced to… 
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