论文标题
katětov-tong定理的新方法
A new approach to the Katětov-Tong theorem
论文作者
论文摘要
我们给出了katětov-tong定理的新证明。我们的策略是首先证明紧凑型Hausdorff空间的定理，然后将其扩展到所有正常空间。关键成分是如何嵌入所有有界实值函数环中的有界连续实现函数的环。在紧凑的情况下，可以通过适当的陈述来描述此嵌入，我们证明这意味着katětov-tong定理和Stone-Weierstrass定理的版本。然后，我们通过展示如何将上半连续实现的函数扩展到石材 - \ V CECH CECH紧凑型，以便保留了函数之间的小于或相等的关系，将Katětov-tong定理扩展到所有正常空间。
We give a new proof of the Katětov-Tong theorem. Our strategy is to first prove the theorem for compact Hausdorff spaces, and then extend it to all normal spaces. The key ingredient is how the ring of bounded continuous real-valued functions embeds in the ring of all bounded real-valued functions. In the compact case this embedding can be described by an appropriate statement, which we prove implies both the Katětov-Tong theorem and a version of the Stone-Weierstrass theorem. We then extend the Katětov-Tong theorem to all normal spaces by showing how to extend upper and lower semicontinuous real-valued functions to the Stone-\v Cech compactification so that the less than or equal relation between the functions is preserved.
