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Constructing the Space of Valuations of a Quasi-Polish Space as a Space of Ideals

Author Matthew de Brecht

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Author Details

Matthew de Brecht
  • Kyoto University, Japan

Funding

This work was supported by JSPS KAKENHI Grant Number 18K11166.

Acknowledgements

We thank the reviewers for carefully reading this paper and providing feedback.

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Matthew de Brecht. Constructing the Space of Valuations of a Quasi-Polish Space as a Space of Ideals. In 30th EACSL Annual Conference on Computer Science Logic (CSL 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 216, pp. 9:1-9:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.CSL.2022.9

Abstract

We construct the space of valuations on a quasi-Polish space in terms of the characterization of quasi-Polish spaces as spaces of ideals of a countable transitive relation. Our construction is closely related to domain theoretical work on the probabilistic powerdomain, and helps illustrate the connections between domain theory and quasi-Polish spaces. Our approach is consistent with previous work on computable measures, and can be formalized within weak formal systems, such as subsystems of second order arithmetic.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Topology
  • Theory of computation → Probabilistic computation
Keywords
  • Quasi-Polish spaces
  • space of valuations
  • domain theory
  • measure theory

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