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- W2080641327 abstract "Many manifolds of fiber bundle sections possess a natural atlas ${ ({U_alpha },{phi _alpha })}$ such that the transition maps ${phi _beta }phi _alpha ^{ - 1}$, in addition to being smooth, are continuous with respect to the bounded weak topology of the model. In this paper we formalize the idea of such manifolds by defining $({C^p},{b^ast })$-manifolds, $({C^p},{b^ast })$-morphisms, etc. We then show that these manifolds admit $({C^p},{b^ast })$-partitions of unity subordinate to certain open covers and that they can be embedded as closed $({C^p},{b^ast })$-submanifolds of their model. A corollary of our work is that for any Banach space $B$, the conjugate space ${B^ast }$ admits smooth partitions of unity subordinate to covers by sets open in the bounded weak-$ast$ topology." @default.
- W2080641327 created "2016-06-24" @default.
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- W2080641327 date "1975-01-01" @default.
- W2080641327 modified "2023-10-18" @default.
- W2080641327 title "Partitions of unity and a closed embedding theorem for $(Csp{p},bsp*)$-manifolds" @default.
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- W2080641327 doi "https://doi.org/10.1090/s0002-9947-1975-0397767-8" @default.
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