[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Springer Nature Link
Log in

Infinitary Addition, Real Numbers, and Taut Monads

  • Published:
Applied Categorical Structures Aims and scope Submit manuscript

A Correction to this article was published on 12 May 2018

This article has been updated

Abstract

We make various observations on infinitary addition in the context of the series monoids introduced in our previous paper on real sets. In particular, we explore additional conditions on such monoids suggested by Tarski’s Arithmetic of Cardinal Algebras, and present a monad-theoretic construction that generalizes our construction of paradoxical real numbers.

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
£29.99 /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 includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Change history

  • 12 May 2018

    In the original publication of the article, Eq. (3.24) was published incorrectly. The corrected equation is given in this correction article. The original article has been corrected.

References

  1. Carboni, A., Johnstone, P.T.: Connected limits, familial representability and Artin glueing. Math. Struct. Comput. Sci. 5, 441–459 (1995)

    Article  MathSciNet  Google Scholar 

  2. Carboni, A., Lack, S., Walters, R.F.C.: Introduction to extensive and distributive categories. J. Pure Appl. Algebra 84, 145–158 (1993)

    Article  MathSciNet  Google Scholar 

  3. Clementino, M.M., Hofmann, D., Janelidze, G.: The monads of classical algebra are seldom weakly cartesian. J. Homotopy Relat. Struct. 9(1), 175–197 (2014)

    Article  MathSciNet  Google Scholar 

  4. Hardy, G.H.: Divergent Series. Clarendon Press, Oxford (1949)

    MATH  Google Scholar 

  5. Higgs, D.: A universal characterization of \([0,\infty ]\). Nederl. Akad. Wetensch. Indag. Math. 40(4), 448–455 (1978)

    Article  MathSciNet  Google Scholar 

  6. Higgs, D.: Axiomatic infinite sums—an algebraic approach to integration theory. In: Proceedings of the Conference on Integration, Topology, and Geometry in Linear Spaces (University of North Carolina, Chapel Hill, NC, 1979), Contemporary Mathematics, vol. 2, pp. 205–212 (1980)

  7. Janelidze, G., Street, R.: Real sets. Tbilisi Math. J. 10(3), 23–49 (2017)

    Article  MathSciNet  Google Scholar 

  8. Kangro, G.: Theory of summability of sequences and series. Math. Anal. 12, 5–70 (1974)

    MathSciNet  Google Scholar 

  9. Manes, E.G.: Implementing collection classes with monads. Math. Struct. Comput. Sci. 8, 231–276 (1998)

    Article  MathSciNet  Google Scholar 

  10. Manes, E.G.: Taut monads and T0-spaces. Theor. Comput. Sci. 275, 79–109 (2002)

    Article  MathSciNet  Google Scholar 

  11. Möbus, A.: Alexandrov compactification of relational algebras. Arch. Math. 40, 526–537 (1983)

    Article  MathSciNet  Google Scholar 

  12. Tarski, A.: Cardinal Algebras. Oxford University Press, New York (1949)

    MATH  Google Scholar 

  13. Tarski, A.: Ordinal Algebras. North-Holland Publishing Company, Amsterdam (1956)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch, 7701, South Africa

    George Janelidze

  2. Mathematics Department, Macquarie University, Sydney, NSW, 2109, Australia

    Ross Street

Authors
  1. George Janelidze
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ross Street
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to George Janelidze.

Additional information

Communicated by Maria Manuel Clementino.

Dedicated to Bob Lowen, creator of APCS.

George Janelidze gratefully acknowledges the support of the South African National Research Foundation. Ross Street gratefully acknowledges the support of Australian Research Council Discovery Grants DP1094883, DP130101969 and DP160101519.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Janelidze, G., Street, R. Infinitary Addition, Real Numbers, and Taut Monads. Appl Categor Struct 26, 1047–1064 (2018). https://doi.org/10.1007/s10485-018-9524-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10485-018-9524-4

Keywords

Mathematics Subject Classification

Search

Navigation