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Smooth Partitions of Unity on Certain C(K) Spaces
Published online by Cambridge University Press: 21 December 2009
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One of the main open problems in the theory of Asplund spaces is whether every Asplund space admits a Fréchet differentiable bump function. This problem is also open for C(K) Asplund spaces, where it is unknown even for C∞-Fréchet smooth bump (a general Asplund space does not always admit C2-Fréchet smooth bump – it suffices to consider ℓ3/2[DGZ2]).
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- Copyright © University College London 2005
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