二维空间完备性基本定理的相互证明

Reciprocal Demonstration of Principal Theorems on Completeness Property of Two-dimensional Space

平面上的5个定理,闭区域套定理,有限覆盖定理,聚点定理,致密性定理及Cauthy准则,刻画了R2的完备性,构成了二元函数极限理论的基础.分别以闭区域套定理,有限覆盖定理,聚点定理为基础,证明其它定理,体现了这5个定理之间的相互等价.

Cauchy Convergence Principle, Accumulation Principle, Bolzano-Weierstrass Theorem, Nested Closed Region Theorem and Finite Covering Principle are equal theorems which depict sequential compactness and completeness of two-dimensional space. The five theorems are absolutely basic for the limit theory on duality functions. This article is to narrate the equipollence by proving every theorem by using Accumulation Principle, Nested Closed Region Theorem and Finite Covering Principle.