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Approximately \(\varGamma \)-semigroups in proximal relator spaces

  • Mustafa Uçkun
  • Ebubekir İnan
Original Paper
  • 9 Downloads

Abstract

This article introduces approximately \(\varGamma \)-semigroups, approximately \(\varGamma \)-ideals and approximately upper \(\varGamma \)-ideals in proximal relator spaces. Some properties of descriptively approximations are investigated using by object description \(\varGamma \)-homomorphism. Furthermore, an example of approximately \(\varGamma \)-semigroup with working on digital images.

Keywords

Proximity spaces Relator spaces Descriptive approximations Approximately semigroups 

Mathematics Subject Classification

08A05 68Q32 54E05 

References

  1. 1.
    Efremovič, V.A.: Infinitesimal spaces. Doklady Akad. Nauk SSSR (N. S.) 76, 341–343 (1951). (Russian) MathSciNetGoogle Scholar
  2. 2.
    İnan, E.: Approximately Groups in Proximal Relator Spaces: An Algebraic View of Digital Images. arXiv:1701.07251v2 (2017)
  3. 3.
    İnan, E.: Approximately semigroups and ideals: an algebraic view of digital images. Afyon Kocatepe Univ. J. Sci. Eng. 17, 479–487 (2017)CrossRefGoogle Scholar
  4. 4.
    Kovăr, M.: A New Causal Topology and Why the Universe is Co-Compact, pp. 1–15. arXiv:1112.0817 [math-ph] (2011)
  5. 5.
    Lodato, M.: On topologically induced generalized proximity relations. Ph.D. Thesis, Rutgers University (1962)Google Scholar
  6. 6.
    Naimpally, S.A., Warrack, B.D.: Proximity Spaces, Cambridge Tract (1970)Google Scholar
  7. 7.
    Naimpally, S.A., Peters, J.F.: Topology with Applications: Topological Spaces Via Near and Far. World Scientific, Singapore (2013)CrossRefGoogle Scholar
  8. 8.
    Peters, J.F., Naimpally, S.A.: Applications of near sets. Not. Am. Math. Soc. 59(4), 536–542 (2012)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Peters, J.F.: Near sets: an introduction. Math. Comput. Sci. 7(1), 3–9 (2013)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Peters, J.F., İnan, E., Öztürk, M.A.: Spatial and descriptive isometries in proximity spaces. Gen. Math. Notes 21(2), 125–134 (2014)Google Scholar
  11. 11.
    Peters, J.F., Öztürk, M.A., Uçkun, M.: Exactness of proximal groupoid homomorphisms. Adıyaman Univ. J. Sci. 5(1), 1–13 (2015)Google Scholar
  12. 12.
    Peters, J.F.: Proximal relator spaces. Filomat 30(2), 469–472 (2016)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Peters, J.F.: Computational Proximity: Excursions in the Topology of Digital Images, Intelligent Systems Reference Library, vol. 102. Springer, Berlin (2016)Google Scholar
  14. 14.
    Sen, M.K., Saha, N.K.: On \(\varGamma \)-semigroup I. Bull. Calcutta Math. Soc. 78(3), 180–186 (1986)MathSciNetGoogle Scholar
  15. 15.
    Száz, Á.: Basic tools and mild continuities in relator spaces. Acta Math. Hungar. 50(3–4), 177–201 (1987)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Arts and SciencesAdıyaman UniversityAdıyamanTurkey

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