Total Representations

TL;DR

This paper advocates for the use of total representations in computable analysis, highlighting their advantages in unifying terminology, simplifying technical aspects, and opening new research directions.

Contribution

It introduces the concept of total representations, contrasting them with partial ones, and discusses their benefits and implications for computable analysis.

Findings

Total representations unify terminology and simplify technical details.

They suggest new invariants of topological spaces.

Open questions are proposed based on total representations.

Abstract

Almost all representations considered in computable analysis are partial. We provide arguments in favor of total representations (by elements of the Baire space). Total representations make the well known analogy between numberings and representations closer, unify some terminology, simplify some technical details, suggest interesting open questions and new invariants of topological spaces relevant to computable analysis.