A characterization for spaces of sections

Manoharan, Palanivel

doi:10.1090/S0002-9939-98-04246-4

A characterization for spaces of sections
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Proc. Amer. Math. Soc. 126 (1998), 1205-1210 Request permission

Abstract:

The space of smooth sections of a bundle over a compact smooth manifold $K$ can be equipped with a manifold structure, called an $A$-manifold, where $A$ represents the Fréchet algebra of real valued smooth functions on $K$. We prove that the $A$-manifold structure characterizes the spaces of sections of bundles over $K$ and its open subspaces. We also describe the $A^{(r)}$-maps between $A$-manifolds.

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