Reconstruction of mapping spaces by inverse limits
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908289789329408 |
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| author | Gao, Jing-Wen Yang, Xiao-Song |
| author_facet | Gao, Jing-Wen Yang, Xiao-Song |
| contents | Extending the results of reconstruction of compact metric spaces by inverse limits, we show that if $(X, d), (Y, d)$ are compact metric spaces, then the mapping space $Y^X$ is homotopy equivalent to the inverse limit of an inverse system of finite $T_0$-spaces which depends only on the finite open covers of $X$ and $Y$. Applying our tools, we obtain that if $H$ is an isotopy of a compact metric space $(X, d)$, then $H_1H^{-1}_0$ can be approximated in terms of moves of a finite $T_0$-space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_22922 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reconstruction of mapping spaces by inverse limits Gao, Jing-Wen Yang, Xiao-Song Combinatorics Extending the results of reconstruction of compact metric spaces by inverse limits, we show that if $(X, d), (Y, d)$ are compact metric spaces, then the mapping space $Y^X$ is homotopy equivalent to the inverse limit of an inverse system of finite $T_0$-spaces which depends only on the finite open covers of $X$ and $Y$. Applying our tools, we obtain that if $H$ is an isotopy of a compact metric space $(X, d)$, then $H_1H^{-1}_0$ can be approximated in terms of moves of a finite $T_0$-space. |
| title | Reconstruction of mapping spaces by inverse limits |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2503.22922 |