A continuous map ℝd → ℝN is k-regular if it maps any k pairwise distinct points to k linearly independent vectors. Our main result on k-regular maps is the following lower bound for the existence of such maps between Euclidean spaces, in which α(k) denotes the number of ones in the dyadic expansion of k: For d ≥ 1 and k ≥ 1 there is no k-regular map ℝd → ℝN for N
CITATION STYLE
Blagojević, P. V. M., Lück, W., & Ziegler, G. M. (2015). On highly regular embeddings. In Springer INdAM Series (Vol. 12, pp. 149–153). Springer International Publishing. https://doi.org/10.1007/978-3-319-20155-9_26
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