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 w.r.t. these numberings, and investigate degree spectra of continuous domains.
翻译:众所周知的、以可计算为基础的领域的理想表述最近扩大到(有效的)准波兰空间。我们继续这些调查,探索一些有效的准波兰空间的类别。特别是,我们证明是准波兰空间域特征的有效版本,描述准波兰地名的有效扩展,发现有效准波兰空间类别的自然编号,估计(有效)原貌关系的复杂性和某些空间类别的复杂性,这些编号,并调查连续域的度谱。