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arXiv · 2503.22922

Reconstruction of mapping spaces by inverse limits

Jing-Wen Gao·Xiao-Song Yang
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Abstract

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.

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Jing-Wen Gao, Xiao-Song Yang. 2025-03-29. Reconstruction of mapping spaces by inverse limits. https://arxiv.org/abs/2503.22922

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