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Quasi-Metric Properties of the Dual Cone of an Asymmetric Normed Space [PDF]
Results in Mathematics, 2022 [EN] We obtain some quasi-metric properties of the dual cone of an asymmetric normed space. Thus, we prove that it is balanced, and hence its topology is completely regular. We also prove that it is complete in the sense of D. Doitchinov.
Carmen Alegre
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Index of symmetry and topological classification of asymmetric normed spaces [PDF]
Rocky Mountain Journal of Mathematics, 2020 International audienceLet $X,Y$ 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.
Mohammed Bachir, Gonzalo Flores
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Extensions of asymmetric norms to linear spaces
2011Summary: Let \(M\) be a subset of a (real) linear space that is closed with respect to the sum of vectors and the product by nonnegative scalars. An asymmetric seminorm on \(M\) is a nonnegative and subadditive positively homogeneous function \(q\) defined on \(M\).
Garcìa-Raffi, L.M. +2 more
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Representation of uniform boundedness principle and Hahn–Banach theorem in linear n-normed space
Journal of Analysis, 2021T K Samanta
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Convex Functions on a Normed Linear Space
CMS Books in Mathematics, 2006Constantin P Niculescu +1 more
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A normed linear space containing the Schlicht functions
Monatshefte Fur Mathematik, 1972J A Pfaltzgraff
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Completeness of fuzzy normed linear space of all weakly fuzzy bounded linear operators
Fuzzy Sets and Systems, 2014exaly