Research Article
BibTex RIS Cite
Year 2024, Volume: 16 Issue: 2, 285 - 298, 31.12.2024
https://doi.org/10.47000/tjmcs.1393985

Abstract

References

  • Arkowitz, M., H-Spaces and Co-H-Spaces, Introduction to Homotopy Theory, Springer, New York, NY, 2011.
  • Boonpok, C. On continuous maps in closure spaces, General Mathematics, 17(2)(2009), 127–134.
  • Cech, E., Topological spaces, Czechoslovak Acad. of Sciences, Prag, 1966.
  • Demiralp, S. Co-hopf space structure on closure spaces, Turkish Journal of Mathematics and Computer Science, 14(2)(2022), 321–330.
  • Demiralp, S., Guner, E.,Some characterizations of Hopf group on fuzzy topological spaces, Iranian Journal of Fuzzy Systems, 11(6)(2014), 111–121.
  • Demiralp, S., Hamouda, E.H., Guner, E., Some properties of fuzzy H-spaces, JP Journal of Algebra, Number Theory and Applications, 40(4)(2018), 429–448.
  • Ege, O., Fuzzy Co-Hopf spaces, Paper presented at the ICMM, University of Fırat, Elazig, 12–14 May 2016, (2016).
  • Ege, O., Karaca, I., Some properties of digital h-spaces, Turkish Journal of Electrical Engineering and Computer Sciences, 24(3)(2016), 1930–1941.
  • Ege, O., Karaca, I., Digital co-hopf spaces, Filomat, 34(8)(2020), 2705–2711.
  • Ege, O., Karaca, I., Digital H-spaces, Proceeding of 3rd International Symposium on Computing in Science and Engineering, October 24-25, 2013, Kusadasi-TURKEY, 133–138.
  • Eroglu, I., Guner, E., Separation axioms in Cech closure ordered spaces, Commun. Fac. Sci. Univ. Ank. Ser A1 Math. Stat., 65(2016), 1–10.
  • Ghanim, M.H., Fatma S. Al-Sirehy, Topological modification of a fuzzy closure space, Fuzzy sets and systems, 27(2)(1988), 211–215.
  • Hacat, G., On fuzzy retract of a fuzzy loop space, International Journal of Mathematics Trends and Technology, 65(2)(2019), 73–82.
  • Hopf, H., Uber die topologie der gruppen-mannigfaltigkeiten und Ihre verallgemeinerungen, The Annals of Mathematics Second Series, 42(1)(1941), 22.
  • Lee, D.W., Near-rings on digital hopf groups, Applicable Algebra in Engineering, Communication and Computing, 29(3) 2018), 261-–282.
  • Lee, D.W., Digital h-spaces and actions in the pointed digital homotopy category, Applicable Algebra in Engineering, Communication and Computing, 31(2)(2020), 149—169.
  • Lee, D.W., Digital hopf spaces and their duals, Journal of Mathematics, 2022(2022).
  • Mahima Ranjan, A., Basic Algebraic Topology and Its Applications, New Delhi, Springer, 2016.
  • Majeed, R.N., Cech fuzzy soft closure spaces, International Journal of Fuzzy System Applications (IJFSA), 7(2)(2018), 62–74.
  • Mashhour, A.S., Ghanim, M.H., On closure spaces, Indian J. pure appl. Math., 14(6)(1983), 680–691.
  • Mashhour, A.S., Ghanim, M.H., Fuzzy closure spaces, Journal of mathematical analysis and applications, 106(1)(1985), 154–170.
  • Mesiar, R., Kolesarova, A., On the fuzzy set theory and aggregation functions: History and some recent advances, Iranian Journal of Fuzzy Systems, 15(7)(2018), 1–12.
  • Park, K., On sub-H-groups of an H group and their duals, Journal of the Korean Mathematical Society, 6(1)(1969), 41–46.
  • Reza, A., Zahedi, M.M., Fuzzy chain complex and fuzzy homotopy, Fuzzy sets and systems, 112(2)(2000), 287–297.
  • Rieser, A., Cech closure spaces: A unified framework for discrete and continuous homotopy, Topology and its Applications, 296(2021), 107613.
  • Sagiroglu, S., Guner, E., Kocyigit, E., Generalized neighborhood systems of fuzzy points, Communications Series A1 Mathematics and Statistics, 62(2)(2013), 67–74.
  • Spanier, Edwin H., Algebraic Topology. Springer Science and Business Media, 1989.
  • Switzer, Robert M., Algebraic Topology-Homotopy and Homology, Springer, 2017.

Fuzzy Closure Hopf Space

Year 2024, Volume: 16 Issue: 2, 285 - 298, 31.12.2024
https://doi.org/10.47000/tjmcs.1393985

Abstract

In this study, we introduce the concepts of fuzzy closure Hopf space and fuzzy closure Hopf group within the framework of fuzzy closure spaces, using homotopy theory. We investigate the relationships between the fuzzy closure Hopf group and its homotopy equivalence. Furthermore, we demonstrate the existence of a contravariant functor from the category of fuzzy closure Hopf spaces and the continuous functions, to the category of groups and homomorphisms. This is demonstrated by illustrating that the set of homotopy function classes among fuzzy closure Hopf groups constitutes a group.

References

  • Arkowitz, M., H-Spaces and Co-H-Spaces, Introduction to Homotopy Theory, Springer, New York, NY, 2011.
  • Boonpok, C. On continuous maps in closure spaces, General Mathematics, 17(2)(2009), 127–134.
  • Cech, E., Topological spaces, Czechoslovak Acad. of Sciences, Prag, 1966.
  • Demiralp, S. Co-hopf space structure on closure spaces, Turkish Journal of Mathematics and Computer Science, 14(2)(2022), 321–330.
  • Demiralp, S., Guner, E.,Some characterizations of Hopf group on fuzzy topological spaces, Iranian Journal of Fuzzy Systems, 11(6)(2014), 111–121.
  • Demiralp, S., Hamouda, E.H., Guner, E., Some properties of fuzzy H-spaces, JP Journal of Algebra, Number Theory and Applications, 40(4)(2018), 429–448.
  • Ege, O., Fuzzy Co-Hopf spaces, Paper presented at the ICMM, University of Fırat, Elazig, 12–14 May 2016, (2016).
  • Ege, O., Karaca, I., Some properties of digital h-spaces, Turkish Journal of Electrical Engineering and Computer Sciences, 24(3)(2016), 1930–1941.
  • Ege, O., Karaca, I., Digital co-hopf spaces, Filomat, 34(8)(2020), 2705–2711.
  • Ege, O., Karaca, I., Digital H-spaces, Proceeding of 3rd International Symposium on Computing in Science and Engineering, October 24-25, 2013, Kusadasi-TURKEY, 133–138.
  • Eroglu, I., Guner, E., Separation axioms in Cech closure ordered spaces, Commun. Fac. Sci. Univ. Ank. Ser A1 Math. Stat., 65(2016), 1–10.
  • Ghanim, M.H., Fatma S. Al-Sirehy, Topological modification of a fuzzy closure space, Fuzzy sets and systems, 27(2)(1988), 211–215.
  • Hacat, G., On fuzzy retract of a fuzzy loop space, International Journal of Mathematics Trends and Technology, 65(2)(2019), 73–82.
  • Hopf, H., Uber die topologie der gruppen-mannigfaltigkeiten und Ihre verallgemeinerungen, The Annals of Mathematics Second Series, 42(1)(1941), 22.
  • Lee, D.W., Near-rings on digital hopf groups, Applicable Algebra in Engineering, Communication and Computing, 29(3) 2018), 261-–282.
  • Lee, D.W., Digital h-spaces and actions in the pointed digital homotopy category, Applicable Algebra in Engineering, Communication and Computing, 31(2)(2020), 149—169.
  • Lee, D.W., Digital hopf spaces and their duals, Journal of Mathematics, 2022(2022).
  • Mahima Ranjan, A., Basic Algebraic Topology and Its Applications, New Delhi, Springer, 2016.
  • Majeed, R.N., Cech fuzzy soft closure spaces, International Journal of Fuzzy System Applications (IJFSA), 7(2)(2018), 62–74.
  • Mashhour, A.S., Ghanim, M.H., On closure spaces, Indian J. pure appl. Math., 14(6)(1983), 680–691.
  • Mashhour, A.S., Ghanim, M.H., Fuzzy closure spaces, Journal of mathematical analysis and applications, 106(1)(1985), 154–170.
  • Mesiar, R., Kolesarova, A., On the fuzzy set theory and aggregation functions: History and some recent advances, Iranian Journal of Fuzzy Systems, 15(7)(2018), 1–12.
  • Park, K., On sub-H-groups of an H group and their duals, Journal of the Korean Mathematical Society, 6(1)(1969), 41–46.
  • Reza, A., Zahedi, M.M., Fuzzy chain complex and fuzzy homotopy, Fuzzy sets and systems, 112(2)(2000), 287–297.
  • Rieser, A., Cech closure spaces: A unified framework for discrete and continuous homotopy, Topology and its Applications, 296(2021), 107613.
  • Sagiroglu, S., Guner, E., Kocyigit, E., Generalized neighborhood systems of fuzzy points, Communications Series A1 Mathematics and Statistics, 62(2)(2013), 67–74.
  • Spanier, Edwin H., Algebraic Topology. Springer Science and Business Media, 1989.
  • Switzer, Robert M., Algebraic Topology-Homotopy and Homology, Springer, 2017.
There are 28 citations in total.

Details

Primary Language English
Subjects Topology
Journal Section Articles
Authors

Sibel Demiralp 0000-0002-3977-587X

Publication Date December 31, 2024
Submission Date November 21, 2023
Acceptance Date March 28, 2024
Published in Issue Year 2024 Volume: 16 Issue: 2

Cite

APA Demiralp, S. (2024). Fuzzy Closure Hopf Space. Turkish Journal of Mathematics and Computer Science, 16(2), 285-298. https://doi.org/10.47000/tjmcs.1393985
AMA Demiralp S. Fuzzy Closure Hopf Space. TJMCS. December 2024;16(2):285-298. doi:10.47000/tjmcs.1393985
Chicago Demiralp, Sibel. “Fuzzy Closure Hopf Space”. Turkish Journal of Mathematics and Computer Science 16, no. 2 (December 2024): 285-98. https://doi.org/10.47000/tjmcs.1393985.
EndNote Demiralp S (December 1, 2024) Fuzzy Closure Hopf Space. Turkish Journal of Mathematics and Computer Science 16 2 285–298.
IEEE S. Demiralp, “Fuzzy Closure Hopf Space”, TJMCS, vol. 16, no. 2, pp. 285–298, 2024, doi: 10.47000/tjmcs.1393985.
ISNAD Demiralp, Sibel. “Fuzzy Closure Hopf Space”. Turkish Journal of Mathematics and Computer Science 16/2 (December 2024), 285-298. https://doi.org/10.47000/tjmcs.1393985.
JAMA Demiralp S. Fuzzy Closure Hopf Space. TJMCS. 2024;16:285–298.
MLA Demiralp, Sibel. “Fuzzy Closure Hopf Space”. Turkish Journal of Mathematics and Computer Science, vol. 16, no. 2, 2024, pp. 285-98, doi:10.47000/tjmcs.1393985.
Vancouver Demiralp S. Fuzzy Closure Hopf Space. TJMCS. 2024;16(2):285-98.