Abstract
The homology of an unknown subspace of Euclidean space can be determined from the intrinsic Čech complex of a sample of points in the subspace, without reference to the ambient Euclidean space. More precisely, given a subspace X of Euclidean space and a sample A of points in X, we give conditions for the homology of X to be isomorphic to a certain persistent homology group of the intrinsic Čech complex.
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