Ideal presentations and numberings of some classes of effective quasi-Polish spaces
Matthew de Brecht, Takayuki Kihara, Takayuki Kihara, Victor Selivanov, Victor Selivanov · Computability · 2024
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.