Ideal presentations and numberings of some classes of effective quasi-Polish spaces-Reference-Cited by-同舟云学术

Ideal presentations and numberings of some classes of effective quasi-Polish spaces

Published:2024-01-29 Issue: Volume: Page:1-24
ISSN:2211-3576
Container-title:Computability
language:
Short-container-title:COM

Author:

de Brecht Matthew¹,Kihara Takayuki²,Selivanov Victor³

Affiliation:

1. Graduate School of Human and Environmental Studies, Kyoto University, Japan

2. Department of Mathematical Informatics, Graduate School of Informatics, Nagoya University, Japan

3. Department of Mathematics and Computer Science, St. Petersburg University, Russia

Abstract

The well known ideal presentations of countably based domains were recently extended to (effective) quasi-Polish spaces. Continuing these investigations, we explore some classes of effective quasi-Polish spaces. In particular, we prove an effective version of the domain-characterization of quasi-Polish spaces, describe effective extensions of quasi-Polish topologies, discover natural numberings of classes of effective quasi-Polish spaces, estimate the complexity of the (effective) homeomorphism relation and of some classes of spaces with respect to these numberings, and investigate degree spectra of continuous domains.

Publisher

IOS Press

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