Title: k-Regular Mappings of 2 n -Dimensional Euclidean Space
Abstract: A continuous mapf: X -* Rn is said to be k-regular if whenever xl,... , Xk are distinct elements of X, then f(xl), ... , f(xk) are linearly independent. The study of k-regular maps is prompted by the theory of Cebysev approximation. The reader is referred to [12, pp. 237-242] for the relationship between these two concepts. Results on existence and nonexistence of k-regular maps can be found in [1], [2], [4]-[7]. In [4], David Handel and Fred Cohen, using algebraic-topological methods, obtained a nonexistence theorem about k-regular mappings of the plane. The object of the present paper is to generalize their result to k-regular mappings of Rn where n is a power of 2. We obtain an improvement upon the following result, for the case n a power of 2.
Publication Year: 1979
Publication Date: 1979-04-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 24
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