Lipschitz-Free Spaces over Manifolds and the Metric Approximation Property

Richard J. Smith; Filip Talimdjioski

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arXiv · 2206.04953

Lipschitz-Free Spaces over Manifolds and the Metric Approximation Property

Richard J. Smith·Filip Talimdjioski

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Abstract

Let $\|\cdot\|$ be a norm on $\mathbb{R}^N$ and let $M$ be a closed $C^1$-submanifold of $\mathbb{R}^N$. Consider the pointed metric space $(M,d)$, where $d$ is the metric given by $d(x,y)=\|x-y\|$, $x,y\in M$. Then the Lipschitz-free space $\mathcal{F}(M)$ has the Metric Approximation Property.

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BibTeX RIS

Richard J. Smith, Filip Talimdjioski. 2022-06-10. Lipschitz-Free Spaces over Manifolds and the Metric Approximation Property. https://arxiv.org/abs/2206.04953

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