Skip to main content
SpringerLink
Log in

Computability on Quasi-Polish Spaces

  • Conference paper
  • First Online:
Descriptional Complexity of Formal Systems (DCFS 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11612))

Included in the following conference series:

Abstract

We investigate the effectivizations of several equivalent definitions of quasi-Polish spaces and study which characterizations hold effectively. Being a computable effectively open image of the Baire space is a robust notion that admits several characterizations. We show that some natural effectivizations of quasi-metric spaces are strictly stronger.

This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 731143

C. Rojas was supported by Marie Curie RISE project CID.

V. Selivanov was supported by Inria program Invited Researcher and the Regional Mathematical Center of Kazan Federal University (project 1.13556.2019/13.1 of the Ministry of Education and Science of Russian Federation).

D.M. Stull was supported by Inria post-doc program.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Abramsky, S.: Domain theory. In: Abramsky, S., Gabbay, D., Maibaum, T.S.E. (eds.) Handbook of Logic in Computer Science. Clarendon Press, Oxford (1994)

    MATH  Google Scholar 

  2. Becher, V., Grigorieff, S.: Borel and Hausdorff hierarchies in topological spaces of choquet games and their effectivization. Math. Struct. Comput. Sci. 25(7), 1490–1519 (2015). https://doi.org/10.1017/S096012951300025X

    Article  MathSciNet  MATH  Google Scholar 

  3. de Brecht, M.: Quasi-polish spaces. Ann. Pure Appl. Logic 164(3), 356–381 (2013)

    Article  MathSciNet  Google Scholar 

  4. Brecht de, M., Pauly, A., Schröder, M.: Overt choice. CoRR abs/1902.05926 (2019). http://arxiv.org/abs/1902.05926

  5. Chen, R.: Notes on quasi-Polish spaces. CoRR abs/1902.05926 (2018). http://arxiv.org/abs/1809.07440

  6. Gao, S.: Invariant Descriptive Set Theory. CRC Press, New York (2009)

    MATH  Google Scholar 

  7. Gregoriades, V.: Classes of polish spaces under effective Borel isomorphism. Mem. Amer. Math. Soc. 240(1135) (2016). https://doi.org/10.1090/memo/1135

  8. Gregoriades, V., Kispéter, T., Pauly, A.: A comparison of concepts from computable analysis and effective descriptive set theory. Math. Struct. Comput. Sci. 27(8), 1414–1436 (2017). https://doi.org/10.1017/S0960129516000128

    Article  MathSciNet  MATH  Google Scholar 

  9. Grubba, T., Schröder, M., Weihrauch, K.: Computable metrization. MLQ Math. Log. Q. 53(4–5), 381–395 (2007). https://doi.org/10.1002/malq.200710009

    Article  MathSciNet  MATH  Google Scholar 

  10. Hoyrup, M.: Genericity of weakly computable objects. Theory Comput. Syst.60(3), 396–420 (2017). https://doi.org/10.1007/s00224-016-9737-6

  11. Kechris, A.S.: Classical Descriptive Set Theory, GTM, vol. 156. Springer, New York (1995). https://doi.org/10.1007/978-1-4612-4190-4

    Book  MATH  Google Scholar 

  12. Korovina, M.V., Kudinov, O.V.: Towards computability over effectively enumerable topological spaces. Electron. Notes Theor. Comput. Sci. 221, 115–125 (2008). https://doi.org/10.1016/j.entcs.2008.12.011

    Article  MathSciNet  MATH  Google Scholar 

  13. Korovina, M., Kudinov, O.: On higher effective descriptive set theory. In: Kari, J., Manea, F., Petre, I. (eds.) CiE 2017. LNCS, vol. 10307, pp. 282–291. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-58741-7_27

    Chapter  Google Scholar 

  14. Louveau, A.: Recursivity and compactness. In: Müller, G.H., Scott, D.S. (eds.) Higher Set Theory. LNM, vol. 669, pp. 303–337. Springer, Heidelberg (1978). https://doi.org/10.1007/BFb0103106

    Chapter  Google Scholar 

  15. Moschovakis, Y.N.: Descriptive Set Theory. Mathematical Surveys and Monographs, Second edition. American Mathematical Society (2009). http://www.math.ucla.edu/~ynm/lectures/dst2009/dst2009.pdf

  16. Rogers Jr., H.: Theory of Recursive Functions and Effective Computability. MIT Press, Cambridge (1987). https://mitpress.mit.edu/books/theory-recursive-functions-and-effective-computability. (Reprint from 1967)

  17. Selivanov, V.: On index sets in the Kleene-Mostowski hierarchy. Trans. Inst. Math. 2, 135–158 (1982). in Russian

    MathSciNet  MATH  Google Scholar 

  18. Selivanov, V.L.: Towards a descriptive set theory for domain-like structures. Theoret. Comput. Sci. 365(3), 258–282 (2006). https://doi.org/10.1016/j.tcs.2006.07.053

  19. Selivanov, V.L.: On the difference hierarchy in countably based T\({}_{\text{0}}\)-spaces. Electron. Notes Theor. Comput. Sci. 221, 257–269 (2008). https://doi.org/10.1016/j.entcs.2008.12.022

  20. Selivanov, V.: Towards the effective descriptive set theory. In: Beckmann, A., Mitrana, V., Soskova, M. (eds.) CiE 2015. LNCS, vol. 9136, pp. 324–333. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20028-6_33

    Chapter  Google Scholar 

  21. Weihrauch, K.: Computable Analysis. Springer, Heidelberg (2000). https://doi.org/10.1007/978-3-642-56999-9

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Université de Lorraine, CNRS, Inria, LORIA, 54000, Nancy, France

    Mathieu Hoyrup & Donald M. Stull

  2. Universidad Andres Bello, Santiago, Chile

    Cristóbal Rojas

  3. A.P. Ershov Institute of Informatics Systems SB RAS, Novosibirsk, Russia

    Victor Selivanov

  4. Kazan Federal University, Kazan, Russia

    Victor Selivanov

Authors
  1. Mathieu Hoyrup
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Cristóbal Rojas
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Victor Selivanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Donald M. Stull
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mathieu Hoyrup .

Editor information

Editors and Affiliations

  1. Slovak Academy of Sciences, Košice, Slovakia

    Michal Hospodár

  2. Slovak Academy of Sciences, Košice, Slovakia

    Galina Jirásková

  3. Saint Mary's University, Halifax, NS, Canada

    Stavros Konstantinidis

Rights and permissions

Reprints and permissions

Copyright information

© 2019 IFIP International Federation for Information Processing

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Hoyrup, M., Rojas, C., Selivanov, V., Stull, D.M. (2019). Computability on Quasi-Polish Spaces. In: Hospodár, M., Jirásková, G., Konstantinidis, S. (eds) Descriptional Complexity of Formal Systems. DCFS 2019. Lecture Notes in Computer Science(), vol 11612. Springer, Cham. https://doi.org/10.1007/978-3-030-23247-4_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-23247-4_13

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-23246-7

  • Online ISBN: 978-3-030-23247-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Societies and partnerships

Search

Navigation