# Taking the path computably travelled

## TL;DR

This paper explores the concept of lowness for paths in Baire and Cantor spaces, establishing their equivalence and linking them to lowness for isomorphism, thereby advancing understanding of computability properties in these spaces.

## Contribution

It introduces the notion of lowness for paths in Baire and Cantor spaces and proves their equivalence along with their connection to lowness for isomorphism.

## Key findings

- Lowness for paths in Baire space and Cantor space are equivalent.
- Lowness for these spaces is also equivalent to lowness for isomorphism.
- The paper establishes foundational relationships between these notions of lowness.

## Abstract

We define a real $A$ to be low for paths in Baire space (or Cantor space) if every $\Pi^0_1$ class with an $A$-computable element has a computable element. We prove that lowness for paths in Baire space and lowness for paths in Cantor space are equivalent and, furthermore, that these notions are also equivalent to lowness for isomorphism.