An epsilon-delta characterization of a certain TTE computability notion

TL;DR

This paper provides a new epsilon-delta based characterization of TTE computability in effective metric spaces, avoiding the traditional reliance on Cauchy representations under certain conditions.

Contribution

It introduces an epsilon-delta characterization of TTE computability that does not depend on representations, broadening the understanding of computability in metric spaces.

Findings

Epsilon-delta characterization aligns with traditional TTE notions

Applicable under weak assumptions on effective metric spaces

Simplifies the conceptual framework for TTE computability

Abstract

The TTE computability notion in effective metric spaces is usually defined by using Cauchy representations. Under some weak assumptions, we characterize this notion in a way which avoids using the representations.