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Pré-Publication, Document De Travail Année : 2020

INDEX OF SYMMETRY AND TOPOLOGICAL CLASSIFICATION OF ASYMMETRIC NORMED SPACES

Résumé

Let $X,Y$ be asymmetric normed spaces and $L_c(X,Y)$ the convex cone of all linear continuous operators from $X$ to $Y$. It is known that in general, $L_c(X,Y)$ is not a vector space. The aim of this note is to give, using the Baire category theorem, a complete cracterization on $X$ and a finite dimensional $Y$ so that $L_c(X,Y)$ is a vector space. For this, we introduce an index of symmetry of the space $X$ denoted $c(X)\in [0,1]$ and we give the link between the index $c(X)$ and the fact that $L_c(X,Y)$ is in turn an asymmetric normed space for every asymmetric normed space $Y$. Our study leads to a topological classification of asymmetric normed spaces.
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Dates et versions

hal-02488691 , version 1 (23-02-2020)
hal-02488691 , version 2 (04-06-2020)

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Mohammed Bachir, G. Flores. INDEX OF SYMMETRY AND TOPOLOGICAL CLASSIFICATION OF ASYMMETRIC NORMED SPACES. 2020. ⟨hal-02488691v2⟩
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