关于满覆盖

On Full Covering

本文引进满覆盖的概念,证明了它与有限覆盖定理的等价性,利用满覆盖定理证明有界闭集上连续函数的一些常见性质.最后,我们将满覆盖概念推广到高维空间的情况.

In this note,we introduce the concept of“full covernig”,which is equivalent to Borel finite covering for describing the completeness of the real number system, and we prove various properties of continnous functions on a bounded closed set by using full covering theorem.Finally,we generalize these discussions to the case of higher dimension space.