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arXiv · 2009.02727

A Study on Nice Open Covers in Constructive Analysis

Tong Cheng·Zhihan Gao·Yuxin Ma·Yuhan Ning·Jianghao Xu
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Abstract

Mathematicians like Markov and Bishop made an effort to develop constructive mathematics and extended many theorems in classical mathematical analysis. Heine Borel theorem tells us that a closed bounded subset of Euclidean space R is compact, but in constructive mathematics, Tseitin and Zaslavskii showed that the set of all constructive real numbers between 0 and 1 is not compact. We are going to show that when giving certain restriction to the open cover on [0,1], we can however always choose a finite sub-cover.

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Tong Cheng, Zhihan Gao, Yuxin Ma, Yuhan Ning, Jianghao Xu. 2020-09-06. A Study on Nice Open Covers in Constructive Analysis. https://arxiv.org/abs/2009.02727

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