Geodesic
Spaces of $CD_0$-functions and $CD_0$-sections of Banach bundles
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 6 (2009), pp. 219-242.

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We first briefly expose some crucial phases in studying the space $CD_0(Q)=C(Q)+c_0(Q)$ whose elements are the sums of continuous and “discrete” functions defined on a compact Hausdorff space $Q$ without isolated points. In this part, special emphasis is on describing the compact space $\widetilde Q$ representing the Banach lattice $CD_0(Q)$ as $C(\widetilde Q)$. The rest of the article is dedicated to the analogous frame related to the space $CD_0(Q,\chi)$ of “continuous-discrete” sections of a Banach bundle $\chi$ and the space of $CD_0$-homomorphisms of Banach bundles.
Keywords: Banach lattice, $AM$-space, Alexandroff duplicate, continuous Banach bundle, section of a Banach bundle, homomorphism of Banach bundles
Mots-clés : Banach $C(Q)$-module, homomorphism of $C(Q)$-modules. 
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     title = {Spaces of $CD_0$-functions and $CD_0$-sections of {Banach} bundles},
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A. E. Gutman; A. V. Koptev. Spaces of $CD_0$-functions and $CD_0$-sections of Banach bundles. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 6 (2009), pp. 219-242. http://geodesic.mathdoc.fr/item/SEMR_2009_6_a12/

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