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T.S.S.R.K. Rao 《Journal of Mathematical Analysis and Applications》2007,328(2):1173-1177
In this paper we consider proximinality questions for higher ordered dual spaces. We show that for a finite dimensional uniformly convex space X, the space C(K,X) is proximinal in all the duals of even order. For any family of uniformly convex Banach spaces {Xα}{α∈Γ} we show that any finite co-dimensional proximinal subspace of X=c0⊕Xα is strongly proximinal in all the duals of even order of X. 相似文献
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Eugenia Cheng 《Applied Categorical Structures》2007,15(4):439-453
We make a definition of ω-precategory which should underlie any definition of weak ω-category. We make a precise definition of pseudo-invertible cells in this setting. We show that in an ω-precategory with all weak duals, every cell is pseudo-invertible. We deduce that in any “sensible” theory of ω-categories, an ω-category with all weak duals is an ω-groupoid. We discuss various examples and open questions involving higher-dimensional tangles and cobordisms.
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