关于博尔苏克的非撤回定理

arXiv - MATH - Classical Analysis and ODEs Pub Date : 2024-07-18 DOI:arxiv-2407.13395

Waldemar Sieg

引用次数: 0

摘要

经典的博尔苏克非缩回定理断言，$\mathbb{R}^n$ 中的单位球不是单位封闭球的连续缩回。我们将证明这样的单位球是单位封闭球的片断连续缩回。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On Borsuk's non-retract theorem

The classical Borsuk's non-retract theorem asserts that a unit sphere in $\mathbb{R}^n$ is not a continuous retract of the unit closed ball. We will show that such a unit sphere is a piecewise continuous retract of the unit closed ball.

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arXiv - MATH - Classical Analysis and ODEs

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