Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymmetric free spaces and canonical asymmetrizations   A construction analogous to that of Godefroy-Kalton for metric spaces allows
to embed isometrically, in a canonical way, every quasi-metric space $(X,d)$ to
an asymmetric normed space $\mathcal{F}_a(X,d)$ (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 $\mathcal{F}_a(X,d)$ coincides
with the nonlinear asymmetric dual of $(X,d)$, that is, the space
$\mathrm{SLip}_0(X,d)$ of semi-Lipschitz 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
$(X,D)$ inherits naturally a canonical asymmetrization coming from its free
space $\mathcal{F}(X)$. This gives rise to a quasi-metric space $(X,D_+)$ and
an asymmetric free space $\mathcal{F}_a(X,D_+)$. The symmetrization of the
latter is isomorphic to the original free space $\mathcal{F}(X)$. The results
of this work are illustrated with explicit examples.

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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: mtrl-th