  The homology of an unknown subspace of Euclidean space can be determined from
the intrinsic \v{C}ech 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 \v{C}ech complex.
