构造性分析中的Nice开覆盖研究
A Study on Nice Open Covers in Constructive Analysis
摘要：
马尔科夫和毕肖普等数学家努力发展建设性数学，并扩展了经典数学分析中的许多定理。Heine Borel定理告诉我们欧几里得空间R的闭有界子集是紧的，但在构造数学中，Tseitin和Zaslavskii证明了0和1之间的所有构造实数的集合不是紧的。我们将证明，当对[0，1]上的开覆盖给予一定的限制时，我们总是可以选择一个有限的子覆盖。
英文摘要：
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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