# Completeness: When Enough is Enough

### Hannes Diener

School of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand### Matthew Hendtlass

School of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand

## Abstract

We investigate the notion of a complete enough metric space that, while classically vacuous, in a constructive setting allows for the generalisation of many theorems to a much wider class of spaces. In doing so, this notion also brings the known body of constructive results significantly closer to that of classical mathematics. Most prominently, we generalise the Kreisel-Lacome-Shoenfield Theorem/Tseytin's Theorem on the continuity of functions in recursive mathematics.

## Cite this article

Hannes Diener, Matthew Hendtlass, Completeness: When Enough is Enough. Doc. Math. 24 (2019), pp. 899–914

DOI 10.4171/DM/696