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Smooth norms that depend locally on finitely many coordinates

Author: Petr Hájek
Journal: Proc. Amer. Math. Soc. 123 (1995), 3817-3821
MSC: Primary 46B20
MathSciNet review: 1285993
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Abstract: We characterize separable normed spaces that admit equivalent $ {C^\infty }$-smooth norms depending locally on finitely many coordinates. It follows, in particular, that such norms exist on any normed space with countable algebraic basis.

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