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

Matthew de Brecht; Takayuki Kihara; Victor Selivanov

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arXiv · 2301.08469

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

Matthew de Brecht·Takayuki Kihara·Victor Selivanov

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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 w.r.t. these numberings, and investigate degree spectra of continuous domains.

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BibTeX RIS

Matthew de Brecht, Takayuki Kihara, Victor Selivanov. 2023-01-20. Ideal presentations and numberings of some classes of effective quasi-Polish spaces. https://arxiv.org/abs/2301.08469

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