Smooth partitions of unity on manifolds

Lloyd, John

doi:10.1090/S0002-9947-1974-0375374-X

Smooth partitions of unity on manifolds
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by John Lloyd

Trans. Amer. Math. Soc. 187 (1974), 249-259

DOI: https://doi.org/10.1090/S0002-9947-1974-0375374-X

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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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Lecture notes on differential calculus