dc.creatorDaniilidis, Aris
dc.creatorSepulcre, Juan Matías
dc.creatorVenegas M., Francisco
dc.date.accessioned2021-12-16T20:24:40Z
dc.date.accessioned2022-01-27T22:46:36Z
dc.date.available2021-12-16T20:24:40Z
dc.date.available2022-01-27T22:46:36Z
dc.date.created2021-12-16T20:24:40Z
dc.date.issued2021
dc.identifierStudia Mathematica Volume 261 Issue 1 Page 55-102 Published 2021
dc.identifier10.4064/sm200527-24-11
dc.identifierhttps://repositorio.uchile.cl/handle/2250/183278
dc.identifier.urihttp://repositorioslatinoamericanos.uchile.cl/handle/2250/3319421
dc.description.abstractA construction analogous to that of Godefroy-Kalton for metric spaces allows one to embed isometrically, in a canonical way, every quasi-metric space (X, d) in an asymmetric normed space F-a (X, d) (its quasi-metric free space, also called asymmetric free space or semi-Lipschitz free space). The quasi-metric free space satisfies a universal property (linearization of semi-Lipschitz functions). The (conic) dual of F-a (X, d) coincides with the non-linear asymmetric dual of (X, d), that is, the space SLip(0)(X, d) of semiLipschitz functions on (X, d), vanishing at a base point. In particular, for the case of a metric space (X, D), the above construction yields its usual free space. On the other hand, every metric space (X, D) naturally inherits a canonical asymmetrization coming from its free space F(X). This gives rise to a quasi-metric space (X, D+) and an asymmetric free space F-a (X, D+) . The symmetrization of the latter is isomorphic to the original free space F(X). The results of this work are illustrated with explicit examples.
dc.languageen
dc.publisherPolish Acad Sciences Inst Mathematics-IMPAN
dc.rightshttp://creativecommons.org/licenses/by-nc-nd/3.0/us/
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 United States
dc.sourceStudia Mathematica
dc.subjectFree space
dc.subjectCanonical asymmetrization
dc.subjectSemi-Lipschitz functions
dc.subjectQuasi-metric space
dc.titleAsymmetric free spaces and canonical asymmetrizations
dc.typeArtículos de revistas


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