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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | https://arxiv.org/abs/2405.19800 |
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| _version_ | 1866913370291044352 |
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| author | Talimdjioski, Filip |
| author_facet | Talimdjioski, Filip |
| contents | Let $T$ be a compact, metrisable and strongly countable-dimensional topological space. Let $\mathcal{M}^T$ be the set of all metrics $d$ on $T$ compatible with its topology, and equip $\mathcal{M}^T$ with the topology of uniform convergence, where the metrics are regarded as functions on $T^2$. We prove that the set $\mathcal{A}^{T,1}$ of metrics $d\in\mathcal{M}^T$ for which the Lipschitz-free space $\mathcal{F}(T,d)$ has the metric approximation property is residual in $\mathcal{M}^T$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_19800 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lipschitz-free spaces over strongly countable-dimensional spaces and approximation properties Talimdjioski, Filip Functional Analysis Primary 46B20, 46B28 Let $T$ be a compact, metrisable and strongly countable-dimensional topological space. Let $\mathcal{M}^T$ be the set of all metrics $d$ on $T$ compatible with its topology, and equip $\mathcal{M}^T$ with the topology of uniform convergence, where the metrics are regarded as functions on $T^2$. We prove that the set $\mathcal{A}^{T,1}$ of metrics $d\in\mathcal{M}^T$ for which the Lipschitz-free space $\mathcal{F}(T,d)$ has the metric approximation property is residual in $\mathcal{M}^T$. |
| title | Lipschitz-free spaces over strongly countable-dimensional spaces and approximation properties |
| topic | Functional Analysis Primary 46B20, 46B28 |
| url | https://arxiv.org/abs/2405.19800 |