Skip to main content

Advertisement

Springer Nature Link
Log in

A new fixed point theorem in domain theory

  • Published:
Natural Computing Aims and scope Submit manuscript

Abstract

We generalize the standard fixed point theorem in domain theory: a dcpo has the fixed point property iff the image of its least deflation has the fixed point property, provided that the least deflation exists. We then turn to the existence of least deflations, showing that they exist in a number of important cases, including the case of compact domains.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Explore related subjects

Discover the latest articles and news from researchers in related subjects, suggested using machine learning.

References

  • Abramsky S, Jung A (1994) Domain theory. Handbook of logic in computer science, vol 3. Oxford University Press, Oxford

    Google Scholar 

  • Davis A (1955) A characterization of complete lattices. Pac J Math 5:311–319

    Article  MathSciNet  Google Scholar 

  • Duffus D, Rival I, Simonovits M (1980) Spanning retracts of a partially ordered set. Discret Math 32:1–7

    Article  MathSciNet  Google Scholar 

  • Edalat A (1997) Domains for computation in mathematics, physics and exact real arithmetic. Bull Symb Logic 3(4):401–452

    Article  MathSciNet  Google Scholar 

  • Martin K (2011) Domain theory and measurement. In: New structures for physics, Lecture notes in physics, vol 813. Springer, pp 491–589

Download references

Acknowledgements

This research was supported by the Naval Research Laboratory.

Author information

Authors and Affiliations

  1. Center for High Assurance Computer Systems (Code 5540), Naval Research Laboratory, Washington, DC, 20375, USA

    Keye Martin & Johnny Feng

Authors
  1. Keye Martin
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Johnny Feng
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Keye Martin.

Ethics declarations

Conflicts of interest

The authors declare that they have no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Martin, K., Feng, J. A new fixed point theorem in domain theory. Nat Comput 18, 901–905 (2019). https://doi.org/10.1007/s11047-018-9672-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11047-018-9672-3

Keywords