# Computability on quasi-Polish spaces

## TL;DR

This paper explores the effective versions of quasi-Polish spaces, examining their characterizations and the strength of various effectivizations, especially in relation to computable open images and quasi-metric spaces.

## Contribution

It provides a detailed analysis of effectivizations of quasi-Polish spaces and compares their robustness and strength in the context of computability theory.

## Key findings

- Effective open images of Baire space are robust and have multiple characterizations.
- Some effectivizations of quasi-metric spaces are strictly stronger than others.
- The study clarifies the relationship between different effective notions of quasi-Polish spaces.

## Abstract

We investigate the effectivizations of several equivalent definitions of quasi-Polish spaces and study which characterizations hold effectively. Being a computable effectively open image of the Baire space is a robust notion that admits several characterizations. We show that some natural effectivizations of quasi-metric spaces are strictly stronger.