2020/09/06 by Tong Cheng, Zhihan Gao, Cheng, Tong +7
Computer Science · #Computability, Logic, AI Algorithms #FOS: Mathematics #General Topology (math.GN) #Logic (math.LO) #Primary 03D78 Secondary 03F60
paper · pdf · doi:10.48550/arxiv.2009.02727
openalex publication_date 2020/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.