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

Issue title: CiE 2022

Guest editors: Ulrich Berger, Johanna Franklin and Elvira Mayordomo

Article type: Research Article

Authors: de Brecht, Matthew^{a; *} | Kihara, Takayuki^b | Selivanov, Victor^c

Affiliations: [a] Graduate School of Human and Environmental Studies, Kyoto University, Japan | [b] Department of Mathematical Informatics, Graduate School of Informatics, Nagoya University, Japan | [c] Department of Mathematics and Computer Science, St. Petersburg University, Russia

Correspondence: [*] Corresponding author. matthew@i.h.kyoto-u.ac.jp.

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.

Keywords: Effective quasi-Polish space, effective domain, numbering, index set, degree spectrum

DOI: 10.3233/COM-230442

Journal: Computability, vol. 13, no. 3-4, pp. 325-348, 2024