Multilateral research on the role of limiting recursive functions in the computability problem

一个函数的值是在无限的计算过程中某处得到的，我们称之为极限递归函数。当人们从“计算”的角度观察数学时，极限递归函数理论起着重要的作用。将此方法应用于数学中的可计算性理论，并与欧几里德不连续函数变为连续函数的一致拓扑方法进行了比较。我们进一步设计了如何在计算机上实现这一理论的一部分。

A function whose value is obtained somewhere in the course of an infinite process of computations is called a limiting recursive function. The theory of limiting recursive functions plays an important role when one observes mathematics from the standpoint of "computation". We have applied it to the computability theory in mathematics, and compared this method with the method of uniform topology, in which a Euclidean discontinuous function turns continuous. We have further devised how to implement a part of this theory on the computer.