Research Article

Topological Group Construction in Proximity and Descriptive Proximity Spaces

Volume: 16 Number: 1 June 30, 2024
EN

Topological Group Construction in Proximity and Descriptive Proximity Spaces

Abstract

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

Keywords

References

  1. Cech, E., Topological Spaces, Publishing House of the Czechoslovak Academy of Sciences, Prague, 1966.
  2. 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.
  3. Efremovic, V.A., The geometry of proximity I, Mat. Sb.(New Series), 31(73)(1952), 189–200.
  4. Hungerford, T., Algebra, Springer-Verlag, New York, 1974.
  5. Husain, T., Introduction to Topological Groups, W. B. Saunders Company, Philadelphia, 1966.
  6. İnan, E., Uçkun, M., Semitopological δ−groups, Hacet. J. Math. Stat., 52(1)(2023), 163–170.
  7. İs, M., Karaca, İ., Some properties on proximal homotopy theory, Filomat, 38(9)(2024), 3137–3156.
  8. Kuratowski, C., Topologie. I, Panstwowe Wydawnictwo Naukowe, Warsaw, 1958.

Details

Primary Language

English

Subjects

Topology

Journal Section

Research Article

Publication Date

June 30, 2024

Submission Date

July 27, 2023

Acceptance Date

May 22, 2024

Published in Issue

Year 2024 Volume: 16 Number: 1

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
1.İs M. Topological Group Construction in Proximity and Descriptive Proximity Spaces. TJMCS. 2024;16(1):206-216. doi:10.47000/tjmcs.1333562
Chicago
İs, Melih. 2024. “Topological Group Construction in Proximity and Descriptive Proximity Spaces”. Turkish Journal of Mathematics and Computer Science 16 (1): 206-16. https://doi.org/10.47000/tjmcs.1333562.
EndNote
İs M (June 1, 2024) Topological Group Construction in Proximity and Descriptive Proximity Spaces. Turkish Journal of Mathematics and Computer Science 16 1 206–216.
IEEE
[1]M. İs, “Topological Group Construction in Proximity and Descriptive Proximity Spaces”, TJMCS, vol. 16, no. 1, pp. 206–216, June 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 (June 1, 2024): 206-216. https://doi.org/10.47000/tjmcs.1333562.
JAMA
1.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, vol. 16, no. 1, June 2024, pp. 206-1, doi:10.47000/tjmcs.1333562.
Vancouver
1.Melih İs. Topological Group Construction in Proximity and Descriptive Proximity Spaces. TJMCS. 2024 Jun. 1;16(1):206-1. doi:10.47000/tjmcs.1333562

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