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La théorie des cônes biréticulés

Alain Goullet de Rugy (1971)

Annales de l'institut Fourier

Soient 𝒮 la classe des cônes convexes saillants faiblement complets et 𝒮 loc la sous-classe de 𝒮 formée des cônes localement compacts de 𝒮 . Dans les dix dernières années, Alfsen, Bauer, Effros, Rogalski et Stormer ont donné de nombreuses propriétés équivalentes entre elles et qui caractérisent dans 𝒮 loc les cônes de Radon 𝔐 + ( T ) des mesures de Radon positives sur un espace compact T . On montre ici que ces propriétés, convenablement interprétées, restent équivalentes dans la sous-classe 𝒮 p b c des cônes presque bien...

Locally flat Banach spaces

Michal Johanis (2009)

Czechoslovak Mathematical Journal

The notion of functions dependent locally on finitely many coordinates plays an important role in the theory of smoothness and renormings on Banach spaces, especially when higher order smoothness is involved. In this note we investigate the structural properties of Banach spaces admitting (arbitrary) bump functions depending locally on finitely many coordinates.

Locally solid topologies on spaces of vector-valued continuous functions

Marian Nowak, Aleksandra Rzepka (2002)

Commentationes Mathematicae Universitatis Carolinae

Let X be a completely regular Hausdorff space and E a real normed space. We examine the general properties of locally solid topologies on the space C b ( X , E ) of all E -valued continuous and bounded functions from X into E . The mutual relationship between locally solid topologies on C b ( X , E ) and C b ( X ) ( = ...

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