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Main Authors: Gao, Jing-Wen, Yang, Xiao-Song
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2503.22922
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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