A Study on Nice Open Covers in Constructive Analysis
Logic
2020-10-01 v2 General Topology
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.
Keywords
Cite
@article{arxiv.2009.02727,
title = {A Study on Nice Open Covers in Constructive Analysis},
author = {Tong Cheng and Zhihan Gao and Yuxin Ma and Yuhan Ning and Jianghao Xu},
journal= {arXiv preprint arXiv:2009.02727},
year = {2020}
}
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4 pages, 0 figures