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

一个函数，其值是在一个无限的计算过程中的某处获得的，称为极限递归函数。极限递归函数理论在人们从“计算”的观点观察数学时起着重要的作用。我们将它应用于数学中的可计算性理论，并将它与欧氏不连续函数连续化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.