论文标题
一项关于建设性分析中良好开放式封面的研究
A Study on Nice Open Covers in Constructive Analysis
论文作者
论文摘要
像马尔可夫和主教这样的数学家努力开发建设性数学，并在经典数学分析中扩展了许多定理。 Heine Borel定理告诉我们，欧几里得空间的封闭界面子集很紧凑，但是在建设性数学中，Tseitin和Zaslavskii表明，0和1之间所有建设性实数的集合并不紧凑。我们将表明，在对[0,1]上的开放式封面提供一定的限制时，我们可以始终选择有限的子覆盖。
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.
