Filtrations induced by continuous functions

@article{Fabio2013FiltrationsIB,
  title={Filtrations induced by continuous functions},
  author={B. D. Fabio and P. Frosini},
  journal={ArXiv},
  year={2013},
  volume={abs/1304.1268}
}
  • B. D. Fabio, P. Frosini
  • Published 2013
  • Mathematics, Computer Science
  • ArXiv
  • Abstract In Persistent Homology and Topology, filtrations are usually given by introducing an ordered collection of sets or a continuous function from a topological space to R n . A natural question arises, whether these approaches are equivalent or not. In this paper we study this problem and prove that, while the answer to the previous question is negative in the general case, the approach by continuous functions is not restrictive with respect to the other, provided that some natural… CONTINUE READING
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