the generic rank formula_23 is defined as the least rank formula_6 such that the closure in the zariski topology of the set of tensors of rank at most formula_6 is the entire space formula_26. in the case of complex tensors, tensors of rank at most formula_23 form a dense set formula_28: every tensor in the aforementioned space is either of rank less than the generic rank, or it is the limit in the euclidean topology of a sequence of tensors from formula_28. in the case of real tensors, the set of tensors of rank at most formula_23 only forms an open set of positive measure in the euclidean topology. there may exist euclidean-open sets of tensors of rank strictly higher than the generic rank. all ranks appearing on open sets in the euclidean topology are called typical ranks. the smallest typical rank is called the generic rank; this definition applies to both complex and real tensors. the generic rank of tensor spaces was initially studied in 1983 by volker strassen.