Skip to main content
SpringerLink
Log in

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

  • Original Paper
  • Published:
Applicable Algebra in Engineering, Communication and Computing Aims and scope

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.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. Efremovič, V.A.: Infinitesimal spaces. Doklady Akad. Nauk SSSR (N. S.) 76, 341–343 (1951). (Russian)

    MathSciNet  Google Scholar 

  2. İnan, E.: Approximately Groups in Proximal Relator Spaces: An Algebraic View of Digital Images. arXiv:1701.07251v2 (2017)

  3. İnan, E.: Approximately semigroups and ideals: an algebraic view of digital images. Afyon Kocatepe Univ. J. Sci. Eng. 17, 479–487 (2017)

    Article  Google Scholar 

  4. Kovăr, M.: A New Causal Topology and Why the Universe is Co-Compact, pp. 1–15. arXiv:1112.0817 [math-ph] (2011)

  5. Lodato, M.: On topologically induced generalized proximity relations. Ph.D. Thesis, Rutgers University (1962)

  6. Naimpally, S.A., Warrack, B.D.: Proximity Spaces, Cambridge Tract (1970)

  7. Naimpally, S.A., Peters, J.F.: Topology with Applications: Topological Spaces Via Near and Far. World Scientific, Singapore (2013)

    Book  MATH  Google Scholar 

  8. Peters, J.F., Naimpally, S.A.: Applications of near sets. Not. Am. Math. Soc. 59(4), 536–542 (2012)

    MathSciNet  MATH  Google Scholar 

  9. Peters, J.F.: Near sets: an introduction. Math. Comput. Sci. 7(1), 3–9 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  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. 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. Peters, J.F.: Proximal relator spaces. Filomat 30(2), 469–472 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  13. Peters, J.F.: Computational Proximity: Excursions in the Topology of Digital Images, Intelligent Systems Reference Library, vol. 102. Springer, Berlin (2016)

  14. Sen, M.K., Saha, N.K.: On \(\varGamma \)-semigroup I. Bull. Calcutta Math. Soc. 78(3), 180–186 (1986)

    MathSciNet  Google Scholar 

  15. Száz, Á.: Basic tools and mild continuities in relator spaces. Acta Math. Hungar. 50(3–4), 177–201 (1987)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Arts and Sciences, Adıyaman University, 02040, Adıyaman, Turkey

    Mustafa Uçkun & Ebubekir İnan

Authors
  1. Mustafa Uçkun
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ebubekir İnan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mustafa Uçkun.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Uçkun, M., İnan, E. Approximately \(\varGamma \)-semigroups in proximal relator spaces. AAECC 30, 299–311 (2019). https://doi.org/10.1007/s00200-018-0374-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00200-018-0374-y

Keywords

Mathematics Subject Classification

Search

Navigation