Proximity of persistence modules and their diagrams

@inproceedings{Chazal2009ProximityOP,
  title={Proximity of persistence modules and their diagrams},
  author={Fr{\'e}d{\'e}ric Chazal and David Cohen-Steiner and Marc Glisse and Leonidas J. Guibas and Steve Oudot},
  booktitle={SCG '09},
  year={2009}
}
Topological persistence has proven to be a key concept for the study of real-valued functions defined over topological spaces. Its validity relies on the fundamental property that the persistence diagrams of nearby functions are close. However, existing stability results are restricted to the case of continuous functions defined over triangulable spaces. In this paper, we present new stability results that do not suffer from the above restrictions. Furthermore, by working at an algebraic level… 
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