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Cerri, A., Fabio, B.D., Ferri, M., Frosini, P. and Landi, C. (2013) Betti Numbers in Multidimensional Persistent Homology Are Stable Functions. Mathematical Methods in the Applied Sciences, 36, 1543-1557.
https://doi.org/10.1002/mma.2704

has been cited by the following article:

• TITLE: A Basic Topological Approach to the Continuity of the Size Function

  AUTHORS: François Dubeau

  KEYWORDS: Size Function, Connexity, Path, Calm Set, Measure Function

  JOURNAL NAME: Advances in Pure Mathematics, Vol.12 No.10, October 26, 2022

  ABSTRACT: We present old and new results about the size function of a set providing simple and complete proofs using basic tools of general topology. For instance, the decomposition of the size function is given and, under the calmness property of a set, the right continuity of the size function with respect to both arguments is established. Finally, a classification of its points of discontinuity is given.