Finiteness of rank invariants of multidimensional persistent homology groups
classification
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cs.ITmath.IT
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conditionfinitenessinvariantsrankbetticontinuousembeddablefunction
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Rank invariants are a parametrized version of Betti numbers of a space multi-filtered by a continuous vector-valued function. In this note we give a sufficient condition for their finiteness. This condition is sharp for spaces embeddable in R^n.
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