Araştırma Makalesi
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Topological Group Construction in Proximity and Descriptive Proximity Spaces

Yıl 2024, Cilt: 16 Sayı: 1, 206 - 216, 30.06.2024
https://doi.org/10.47000/tjmcs.1333562

Öz

This paper introduces the topological group structure in proximity and especially descriptive proximity
spaces, that is, the concepts of proximal group and descriptive proximal group are introduced. In addition,
the concepts of homomorphism and isomorphism, which give important results in group theory, are discussed by interpreting the concepts of continuity in the theory of (descriptive) proximity

Kaynakça

  • Cech, E., Topological Spaces, Publishing House of the Czechoslovak Academy of Sciences, Prague, 1966.
  • Di Concilio, A., Guadagni, C., Peters, J.F., Ramanna, S., Descriptive proximities. Properties and interplay between classical proximities and overlap, Math. Comput. Sci., 12(1)(2018), 91–106.
  • Efremovic, V.A., The geometry of proximity I, Mat. Sb.(New Series), 31(73)(1952), 189–200.
  • Hungerford, T., Algebra, Springer-Verlag, New York, 1974.
  • Husain, T., Introduction to Topological Groups, W. B. Saunders Company, Philadelphia, 1966.
  • İnan, E., Uçkun, M., Semitopological δ−groups, Hacet. J. Math. Stat., 52(1)(2023), 163–170.
  • İs, M., Karaca, İ., Some properties on proximal homotopy theory, Filomat, 38(9)(2024), 3137–3156.
  • Kuratowski, C., Topologie. I, Panstwowe Wydawnictwo Naukowe, Warsaw, 1958.
  • Leader, S., On products of proximity spaces, Math. Ann., 154(1964), 185–194.
  • Lodato, M.W., On topologically induced generalized proximity relations, Proc. Amer. Math. Soc., 15(1964), 417–422.
  • Maheswari, A., Ilango, G., Topological near groups, Asian Res. J. Math., 18(12)(2022), 46–56.
  • Maheswari, A., Ilango, G., Topological near homomorphisms, J. Res. Appl. Math., 9(2)(2023), 46–54.
  • Naimpally, S.A., Warrack, B.D., Proximity Spaces, Cambridge Tract in Mathematics No. 59, Cambridge University Press, Cambridge, UK, Paperback 2008, MR0278261 1970.
  • Naimpally, S.A., Peters, J.F., Topology With Applications. Topological Spaces via Near and Far, World Scientific, Singapore, 2013.
  • Peters, J.F., Near sets. General theory about nearness of objects, Appl. Math. Sci., 1(53)(2007), 2609–2629.
  • Peters, J.F., Near sets. Special theory about nearness of objects, Fundam. Inform., 75(1-4)(2007), 407–433.
  • Peters, J.F., Near sets: An introduction, Math. Comput. Sci., 7(1)(2013), 3–9.
  • Peters, J.F., Topology of Digital Images: Visual Pattern Discovery in Proximity Spaces (Vol. 63), Springer Science & Business Media, 2014.
  • Peters, J.F., Foundations of Computer Vision: Computational Geometry, Visual Image Structures and Object Shape Detection (Vol. 124), Springer Science & Business Media, 2017.
  • Peters J.F., Vergili, T., Good coverings of proximal Alexandrov spaces. Path cycles in the extension of the Mitsuishi-Yamaguchi good covering ond Jordan Curve Theorems, Appl. Gen. Topol., 24(1)(2023), 25–45.
  • Peters, J.F. Vergili, T., Proximity Space Categories. Results For Proximal Lyusternik-Schnirel’man, Csaszar And Bornology Categories., Submitted, 2023.
  • Riesz, F., Stetigkeitsbegriff und abstrakte mengenlehre, Atti del IV Congresso Internazionale dei Matematici II, 1908.
  • Smirnov, Y.M., On proximity spaces, Mat. Sb.(New Series), 31(73)(1952), 543–574. English Translation: Amer. Math. Soc. Trans.: Series 2, 38(1964), 5–35.
  • Wallace, A.D., Separation space, Ann. Math., (1941), 687–697.
Yıl 2024, Cilt: 16 Sayı: 1, 206 - 216, 30.06.2024
https://doi.org/10.47000/tjmcs.1333562

Öz

Kaynakça

  • Cech, E., Topological Spaces, Publishing House of the Czechoslovak Academy of Sciences, Prague, 1966.
  • Di Concilio, A., Guadagni, C., Peters, J.F., Ramanna, S., Descriptive proximities. Properties and interplay between classical proximities and overlap, Math. Comput. Sci., 12(1)(2018), 91–106.
  • Efremovic, V.A., The geometry of proximity I, Mat. Sb.(New Series), 31(73)(1952), 189–200.
  • Hungerford, T., Algebra, Springer-Verlag, New York, 1974.
  • Husain, T., Introduction to Topological Groups, W. B. Saunders Company, Philadelphia, 1966.
  • İnan, E., Uçkun, M., Semitopological δ−groups, Hacet. J. Math. Stat., 52(1)(2023), 163–170.
  • İs, M., Karaca, İ., Some properties on proximal homotopy theory, Filomat, 38(9)(2024), 3137–3156.
  • Kuratowski, C., Topologie. I, Panstwowe Wydawnictwo Naukowe, Warsaw, 1958.
  • Leader, S., On products of proximity spaces, Math. Ann., 154(1964), 185–194.
  • Lodato, M.W., On topologically induced generalized proximity relations, Proc. Amer. Math. Soc., 15(1964), 417–422.
  • Maheswari, A., Ilango, G., Topological near groups, Asian Res. J. Math., 18(12)(2022), 46–56.
  • Maheswari, A., Ilango, G., Topological near homomorphisms, J. Res. Appl. Math., 9(2)(2023), 46–54.
  • Naimpally, S.A., Warrack, B.D., Proximity Spaces, Cambridge Tract in Mathematics No. 59, Cambridge University Press, Cambridge, UK, Paperback 2008, MR0278261 1970.
  • Naimpally, S.A., Peters, J.F., Topology With Applications. Topological Spaces via Near and Far, World Scientific, Singapore, 2013.
  • Peters, J.F., Near sets. General theory about nearness of objects, Appl. Math. Sci., 1(53)(2007), 2609–2629.
  • Peters, J.F., Near sets. Special theory about nearness of objects, Fundam. Inform., 75(1-4)(2007), 407–433.
  • Peters, J.F., Near sets: An introduction, Math. Comput. Sci., 7(1)(2013), 3–9.
  • Peters, J.F., Topology of Digital Images: Visual Pattern Discovery in Proximity Spaces (Vol. 63), Springer Science & Business Media, 2014.
  • Peters, J.F., Foundations of Computer Vision: Computational Geometry, Visual Image Structures and Object Shape Detection (Vol. 124), Springer Science & Business Media, 2017.
  • Peters J.F., Vergili, T., Good coverings of proximal Alexandrov spaces. Path cycles in the extension of the Mitsuishi-Yamaguchi good covering ond Jordan Curve Theorems, Appl. Gen. Topol., 24(1)(2023), 25–45.
  • Peters, J.F. Vergili, T., Proximity Space Categories. Results For Proximal Lyusternik-Schnirel’man, Csaszar And Bornology Categories., Submitted, 2023.
  • Riesz, F., Stetigkeitsbegriff und abstrakte mengenlehre, Atti del IV Congresso Internazionale dei Matematici II, 1908.
  • Smirnov, Y.M., On proximity spaces, Mat. Sb.(New Series), 31(73)(1952), 543–574. English Translation: Amer. Math. Soc. Trans.: Series 2, 38(1964), 5–35.
  • Wallace, A.D., Separation space, Ann. Math., (1941), 687–697.
Toplam 24 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Topoloji
Bölüm Makaleler
Yazarlar

Melih İs 0000-0002-1272-6701

Yayımlanma Tarihi 30 Haziran 2024
Yayımlandığı Sayı Yıl 2024 Cilt: 16 Sayı: 1

Kaynak Göster

APA İs, M. (2024). Topological Group Construction in Proximity and Descriptive Proximity Spaces. Turkish Journal of Mathematics and Computer Science, 16(1), 206-216. https://doi.org/10.47000/tjmcs.1333562
AMA İs M. Topological Group Construction in Proximity and Descriptive Proximity Spaces. TJMCS. Haziran 2024;16(1):206-216. doi:10.47000/tjmcs.1333562
Chicago İs, Melih. “Topological Group Construction in Proximity and Descriptive Proximity Spaces”. Turkish Journal of Mathematics and Computer Science 16, sy. 1 (Haziran 2024): 206-16. https://doi.org/10.47000/tjmcs.1333562.
EndNote İs M (01 Haziran 2024) Topological Group Construction in Proximity and Descriptive Proximity Spaces. Turkish Journal of Mathematics and Computer Science 16 1 206–216.
IEEE M. İs, “Topological Group Construction in Proximity and Descriptive Proximity Spaces”, TJMCS, c. 16, sy. 1, ss. 206–216, 2024, doi: 10.47000/tjmcs.1333562.
ISNAD İs, Melih. “Topological Group Construction in Proximity and Descriptive Proximity Spaces”. Turkish Journal of Mathematics and Computer Science 16/1 (Haziran 2024), 206-216. https://doi.org/10.47000/tjmcs.1333562.
JAMA İs M. Topological Group Construction in Proximity and Descriptive Proximity Spaces. TJMCS. 2024;16:206–216.
MLA İs, Melih. “Topological Group Construction in Proximity and Descriptive Proximity Spaces”. Turkish Journal of Mathematics and Computer Science, c. 16, sy. 1, 2024, ss. 206-1, doi:10.47000/tjmcs.1333562.
Vancouver İs M. Topological Group Construction in Proximity and Descriptive Proximity Spaces. TJMCS. 2024;16(1):206-1.