منابع مشابه
Saturating Constructions for Normed Spaces
We prove several results of the following type: given finite dimensional normed space V there exists another space X with log dimX = O(log dimV ) and such that every subspace (or quotient) of X, whose dimension is not “too small,” contains a further subspace isometric to V . This sheds new light on the structure of such large subspaces or quotients (resp., large sections or projections of conve...
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We prove several results of the following type: given finite dimensional normed space V possessing certain geometric property there exists another space X having the same property and such that (1) log dimX = O(log dimV ) and (2) every subspace of X, whose dimension is not “too small,” contains a further wellcomplemented subspace nearly isometric to V . This sheds new light on the structure of ...
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Let AR,q denote a family of covering codes, in which the covering radius R and the size q of the underlying Galois field are fixed, while the code length tends to infinity. The construction of families with small asymptotic covering densities is a classical problem in the area Covering Codes. In this paper, infinite sets of families AR,q, where R is fixed but q ranges over an infinite set of pr...
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We show that, for a positive integer r, every minimal 1-saturating set in PG(r − 1, 2) of size at least 11 36 2r + 3 either is a complete cap or can be obtained from a complete cap S by fixing some s ∈ S and replacing every point s ∈ S \ {s} by the third point on the line through s and s. Stated algebraically: if G is an elementary abelian 2-group and a set A ⊆ G \ {0} with |A| > 11 36 |G| + 3 ...
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ژورنال
عنوان ژورنال: Journal of Homotopy and Related Structures
سال: 2013
ISSN: 2193-8407,1512-2891
DOI: 10.1007/s40062-013-0025-8