Surjections on grassmannians preserving pairs of elements with bounded distance
Let m and k be two fixed positive integers such that m > k >= 2. Let V be a left vector space over a division ring with dimension at least m + k + 1. Let G(m) (V) be the Grassmannian consisting of all m-dimensional subspaces of V. We characterize surjective mappings T from g, (V) onto itself s...
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| Format: | Article |
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Elsevier
2010
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| Online Access: | http://eprints.um.edu.my/14980/ |
| Summary: | Let m and k be two fixed positive integers such that m > k >= 2. Let V be a left vector space over a division ring with dimension at least m + k + 1. Let G(m) (V) be the Grassmannian consisting of all m-dimensional subspaces of V. We characterize surjective mappings T from g, (V) onto itself such that for any A, B in 9,,(V), the distance between A and B is not greater than k if and only if the distance between T(A) and T(B) is not greater than k. (C) 2009 Elsevier Inc. All rights reserved. |
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