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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Smooth partitions of unity on manifolds


Author: John Lloyd
Journal: Trans. Amer. Math. Soc. 187 (1974), 249-259
MSC: Primary 58C20
DOI: https://doi.org/10.1090/S0002-9947-1974-0375374-X
MathSciNet review: 0375374
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Abstract: This paper continues the study of the smoothness properties of (real) topological linear spaces. First, the smoothness results previously obtained about various important classes of locally convex spaces, such as Schwartz spaces, are improved. Then, following the ideas of Bonic and Frampton, we use these results to give sufficient conditions for the existence of smooth partitions of unity on manifolds modelled on topological linear spaces.


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DOI: https://doi.org/10.1090/S0002-9947-1974-0375374-X
Keywords: Smooth partitions of unity, Schwartz space, nuclear space, Fréchet derivative, Hadamard derivative
Article copyright: © Copyright 1974 American Mathematical Society