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Semigroups of Relatively Continuous Binary Relations and Their Isomorphisms

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Abstract

All isomorphisms between semigroups of relatively continuous binary relations defined on arbitrary topological spaces are described. As a corollary, the absolute definability of any nontrivial topological space by the semigroup of all of its relatively continuous binary relations is proved.

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References

  1. L. Gillman and M. Jerison, Rings of Continuous Functions (Springer- Verlag, New York, 1960).

    Book  MATH  Google Scholar 

  2. I. M. Gel’fand and A. N. Kolmogorov, “On rings of continuous functions on topological spaces,” Dokl. Akad. Nauk SSSR 22 (1), 11–15 (1939).

    Google Scholar 

  3. E. M. Vechtomov, “Questions on the determination of topological spaces by algebraic systems of continuous functions,” J. Soviet Math. 53 (2), 123–147 (1991).

    Article  MathSciNet  Google Scholar 

  4. E. M. Vechtomov, “The semiring of continuous correspondences on topological spaces,” in Algebra, Number Theory, and Discrete Geometry: Modern Problems, Applications, and Problems of History: Materials of the XVIII International Conference Dedicated to the Centenary of the Birth of Professors B. M. Bredikhin, V. I. Nechaev, and S. B. Stechkin (Tulskii Gos. Pedag. Univ. im. L. N. Tolstogo, Tula, 2020), pp. 100–102 [in Russian].

    Google Scholar 

  5. A. I. Mal’cev, Algebraic Systems (Akademie-Verlag, Berlin, 1973).

    Book  Google Scholar 

  6. J. Riguet, “Relations binaires, fermetures, correspondances de Galois,” Bull. Soc. Math. France 76, 114–155 (1948).

    Article  MathSciNet  MATH  Google Scholar 

  7. R. Engelking, General Topology (Berlin, Heldermann-Verlag, 1989).

    MATH  Google Scholar 

  8. K. D. Maggil, “Isomorphisms of triform semigroups,” J. Austral. Math. Soc. 10, 185–193 (1969).

    Article  MathSciNet  Google Scholar 

  9. S. B. O’Reilly, “The characteristic semigroup of a topological space,” General Topology and Appl. 5 (2), 92–106 (1975).

    MathSciNet  MATH  Google Scholar 

  10. K. D. Maggil, “A survey of semigroups of continuous selfmaps,” Semigroup Forum 11 (3), 189–282 (1976).

    MathSciNet  Google Scholar 

  11. J. S. Golan, Semirings and Their Applications (Kluwer Acad. Publ., Dordrecht, 1999).

    Book  MATH  Google Scholar 

  12. E. M. Vechtomov, “Isomorphisms of semirings of continuous binary relations on topological spaces,” Semigroup Forum 106 (1), 327–331 (2023).

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Vyatka State University, Kirov, 610000, Russia

    V. I. Varankina & E. M. Vechtomov

Authors
  1. V. I. Varankina
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  2. E. M. Vechtomov
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Correspondence to E. M. Vechtomov.

Additional information

Translated from Matematicheskie Zametki, 2023, Vol. 113, pp. 807–819 https://doi.org/10.4213/mzm13854.

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Varankina, V.I., Vechtomov, E.M. Semigroups of Relatively Continuous Binary Relations and Their Isomorphisms. Math Notes 113, 760–769 (2023). https://doi.org/10.1134/S0001434623050176

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  • DOI: https://doi.org/10.1134/S0001434623050176

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