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
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.
