Recursively Countable Subsets of Recursive Metric Spaces

摘要

The subset of a recursive metric space, M, is defined as recursively enumerable (r.e.) if it is the range of a recursive sequence of elements of M. It is recursively countable if it is a subset of an r.e. subset of M. It is known that if M satisfies certain conditions, the range of an effective map from a recursively enumerable set of natural numbers into M is 'thin' in the sense that its complement is dense in M. This study places conditions on a set I of natural numbers that will guarantee that the image of every effective mapping from I into M will be thin in that sense. (Author)