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Remarks Concerning Certain Function Rings in Pointfree Topology

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Abstract

For the \(\ell \)-ring F(L) introduced in Karimi Feizabadi et al. (Categ Gen Algebr Struct Appl 5:85–102, 2016) and then shown to have an embedding into the familiar \(\ell \)-ring \({\mathfrak R}L\) of all real-valued continuous function on a frame L, the resulting image \({\mathfrak S}L\) in \({\mathfrak R}L\) is characterized here by internal properties within \({\mathfrak R}L\). Further, a number of results concerning the \({\mathfrak S}L\) are obtained on the basis of this characterization.

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References

  1. Ball, R.N., Walters-Wayland, J.: $C$- and $C^*$-quotients in pointfree topology. Rozprawy Mat. 412, 1–62 (2002)

    MathSciNet  MATH  Google Scholar 

  2. Banaschewski, B.: The Real Numbers in Pointfree Topology. Textos de Matemática, Serie B, vol. 12. Departamento de Matemático da Universidade de Coimbra, Coimbra (1997)

  3. Banaschewski, B.: On the function ring functor in pointfree topology. Appl. Categ. Struct. 13, 305–328 (2005)

    Article  MathSciNet  Google Scholar 

  4. Banaschewski, B.: Countable composition closedness and integer-valued continuous functions in pointfree topology. Categ. Gen. Algebr. Struct. Appl. 1, 1–9 (2013)

    MATH  Google Scholar 

  5. Banaschewski, B.: On the maps of pointfree topology which preserve the rings of integer-valued continuous functions. Appl. Categ. Struct. (to appear)

  6. Gillman, L., Jerison, M.: Rings of Continuous Functions. Van Nostrand, New York (1960)

    Book  Google Scholar 

  7. Karimi Feizabadi, A., Estaji, A.A., Zarghani, M.: The ring of real-valued functions on a frame. Categ. Gen. Algebr. Struct. Appl. 5, 85–102 (2016)

    MathSciNet  MATH  Google Scholar 

  8. Picado, J., Pultr, A.: Frames and Locales. Springer, Basel (2012)

    Book  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Statistics, McMaster University, Hamilton, ON, L8S 4K1, Canada

    B. Banaschewski

Authors
  1. B. Banaschewski
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Correspondence to B. Banaschewski.

Additional information

Communicated by Eva Colebunders.

Dedicated to my dear friend Robert Lowen on the occasion of his 70th birthday, with special thanks for his manifold contributions to mathematics.

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Banaschewski, B. Remarks Concerning Certain Function Rings in Pointfree Topology. Appl Categor Struct 26, 873–881 (2018). https://doi.org/10.1007/s10485-018-9514-6

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  • DOI: https://doi.org/10.1007/s10485-018-9514-6

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