TY - JOUR

T1 - Ideal presentations and numberings of some classes of effective quasi-Polish spaces

AU - Селиванов, Виктор Львович

AU - de Brecht, Matthew

AU - Kihara, Takayuki

N1 - Matthew de Brecht, Takayuki Kihara, Victor Selivanov. Ideal presentations and numberings of some classes of effective quasi-Polish spaces. Computability, 13 (2024), DOI: 10.3233/COM-230442, vol. Pre-press, no. Pre-press, pp. 1-24, 2024

PY - 2024

Y1 - 2024

N2 - 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.

AB - 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.

UR - https://www.mendeley.com/catalogue/69d7ef10-719f-3dde-9247-6d2dc913b421/

U2 - 10.3233/COM-230442

DO - 10.3233/COM-230442

M3 - Article

JO - Computability

JF - Computability

SN - 2211-3568

ER -