Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2020, Cilt: 49 Sayı: 4, 1414 - 1422, 06.08.2020
https://doi.org/10.15672/hujms.559796

Öz

Kaynakça

  • [1] J.I. Berstein and T. Ganea, The category of a map and of a cohomology class, Fund. Math. 50, 265–279, 1961.
  • [2] C. Berge, Graphs and hypergraphs, 2nd edition, North-Holland, Amsterdam, 1976.
  • [3] A. Borat and T. Vergili, Digital Lusternik-Schnirelmann category, Turkish J. Math. 42 (4), 1845–1852, 2018.
  • [4] L. Boxer, Digitally continuous functions, Pattern Recognit. Lett. 15, 833–839, 1994.
  • [5] L. Boxer, A classical construction for the digital fundamental group, J. Math. Imaging Vision, 10, 51–62, 1999.
  • [6] L. Boxer, Properties of digital homotopy, J. Math. Imaging Vision, 22, 19–26, 2005.
  • [7] L. Boxer, Homotopy properties of sphere-like digital images, J. Math. Imaging Vision, 24, 167–175, 2006.
  • [8] L. Boxer, Digital Products, Wedges, and Covering Spaces, J. Math. Imaging Vision, 25, 159–171, 2006.
  • [9] L. Boxer, Continuous maps on digital simple closed curves, Appl. Math. 1, 377–386, 2010.
  • [10] L. Boxer, Alternate Product Adjacencies in Digital Topology, Appl. Gen. Topol. 19 (1), 21–53, 2018.
  • [11] O. Cornea, G. Lupton, J. Oprea and D. Tanre, Lusternik-Schnirelmann category, in: Mathematical Surveys and Monographs Vol. 103, American Mathematical Society, 2003.
  • [12] T.T. Dieck, Algebraic Topology, European Mathematical Society, 2008.
  • [13] M. Farber, Topological complexity of motion planning, Discrete Comput. Geom. 29, 211–221, 2003.
  • [14] R.H. Fox, On the Lusternik-Schnirelmann category, Ann. of Math. 42, 333–370, 1941.
  • [15] S.E. Han, Computer topology and its applications, Honam Math. J. 25, 153–162, 2003.
  • [16] S.E. Han, Non-product property of the digital fundamental group, Inform. Sci. 171 (1-3), 73–91, 2005.
  • [17] G.T. Herman, Oriented surfaces in digital spaces, CVGIP: Graphical Models and Image Processing, 55, 381–396, 1993.
  • [18] I.M. James, On category in the sense of Lusternik-Schnirelmann, Topology, 17, 331– 348, 1978.
  • [19] I. Karaca and M. Is, Digital topological complexity numbers, Turkish J. Math. 42 (6), 3173–3181, 2018.
  • [20] E. Khalimsky, Motion, deformation, and homotopy in finite spaces, Proceedings IEEE International Conference on Systems, Man, and Cybernetics, 227–234, 1987.
  • [21] L. Lusternik and L. Schnirelmann, Methodes topologiques dans les problemes variationnels, Institute for Mathematics and Mechanics, Moscow, 1930. (In Russian)
  • [22] G. Sabidussi, Graph multiplication, Math. Z. 72, 446–457, 1960.
  • [23] N.A. Scoville and W. Swei, On the Lusternik-Schnirelmann category of a simplicial map, Topology Appl. 216, 116–128, 2017.
  • [24] D. Stanley, On the Lusternik-Schnirelmann category of maps, Canad. J. Math. 54 (3), 608–633, 2002.

Digital Lusternik-Schnirelmann category of digital functions

Yıl 2020, Cilt: 49 Sayı: 4, 1414 - 1422, 06.08.2020
https://doi.org/10.15672/hujms.559796

Öz

Roughly speaking, the digital Lusternik-Schnirelmann category of digital images studies how far a digital image is away from being digitally contractible. The digital Lusternik-Schnirelmann category (digital LS category, for short) is defined in [A. Borat and T. Vergili, Digital Lusternik-Schnirelmann category, Turkish J. Math. 2018]. In this paper, we introduce the digital LS category of digital functions. We will give some basic properties and discuss how this new concept will behave if we change the adjacency relation in the domain and in the image of the digital function and discuss its relation with the digital LS category of a digital image.

Kaynakça

  • [1] J.I. Berstein and T. Ganea, The category of a map and of a cohomology class, Fund. Math. 50, 265–279, 1961.
  • [2] C. Berge, Graphs and hypergraphs, 2nd edition, North-Holland, Amsterdam, 1976.
  • [3] A. Borat and T. Vergili, Digital Lusternik-Schnirelmann category, Turkish J. Math. 42 (4), 1845–1852, 2018.
  • [4] L. Boxer, Digitally continuous functions, Pattern Recognit. Lett. 15, 833–839, 1994.
  • [5] L. Boxer, A classical construction for the digital fundamental group, J. Math. Imaging Vision, 10, 51–62, 1999.
  • [6] L. Boxer, Properties of digital homotopy, J. Math. Imaging Vision, 22, 19–26, 2005.
  • [7] L. Boxer, Homotopy properties of sphere-like digital images, J. Math. Imaging Vision, 24, 167–175, 2006.
  • [8] L. Boxer, Digital Products, Wedges, and Covering Spaces, J. Math. Imaging Vision, 25, 159–171, 2006.
  • [9] L. Boxer, Continuous maps on digital simple closed curves, Appl. Math. 1, 377–386, 2010.
  • [10] L. Boxer, Alternate Product Adjacencies in Digital Topology, Appl. Gen. Topol. 19 (1), 21–53, 2018.
  • [11] O. Cornea, G. Lupton, J. Oprea and D. Tanre, Lusternik-Schnirelmann category, in: Mathematical Surveys and Monographs Vol. 103, American Mathematical Society, 2003.
  • [12] T.T. Dieck, Algebraic Topology, European Mathematical Society, 2008.
  • [13] M. Farber, Topological complexity of motion planning, Discrete Comput. Geom. 29, 211–221, 2003.
  • [14] R.H. Fox, On the Lusternik-Schnirelmann category, Ann. of Math. 42, 333–370, 1941.
  • [15] S.E. Han, Computer topology and its applications, Honam Math. J. 25, 153–162, 2003.
  • [16] S.E. Han, Non-product property of the digital fundamental group, Inform. Sci. 171 (1-3), 73–91, 2005.
  • [17] G.T. Herman, Oriented surfaces in digital spaces, CVGIP: Graphical Models and Image Processing, 55, 381–396, 1993.
  • [18] I.M. James, On category in the sense of Lusternik-Schnirelmann, Topology, 17, 331– 348, 1978.
  • [19] I. Karaca and M. Is, Digital topological complexity numbers, Turkish J. Math. 42 (6), 3173–3181, 2018.
  • [20] E. Khalimsky, Motion, deformation, and homotopy in finite spaces, Proceedings IEEE International Conference on Systems, Man, and Cybernetics, 227–234, 1987.
  • [21] L. Lusternik and L. Schnirelmann, Methodes topologiques dans les problemes variationnels, Institute for Mathematics and Mechanics, Moscow, 1930. (In Russian)
  • [22] G. Sabidussi, Graph multiplication, Math. Z. 72, 446–457, 1960.
  • [23] N.A. Scoville and W. Swei, On the Lusternik-Schnirelmann category of a simplicial map, Topology Appl. 216, 116–128, 2017.
  • [24] D. Stanley, On the Lusternik-Schnirelmann category of maps, Canad. J. Math. 54 (3), 608–633, 2002.
Toplam 24 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Tane Vergili 0000-0003-1821-6697

Ayse Borat 0000-0002-5628-7798

Yayımlanma Tarihi 6 Ağustos 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 49 Sayı: 4

Kaynak Göster

APA Vergili, T., & Borat, A. (2020). Digital Lusternik-Schnirelmann category of digital functions. Hacettepe Journal of Mathematics and Statistics, 49(4), 1414-1422. https://doi.org/10.15672/hujms.559796
AMA Vergili T, Borat A. Digital Lusternik-Schnirelmann category of digital functions. Hacettepe Journal of Mathematics and Statistics. Ağustos 2020;49(4):1414-1422. doi:10.15672/hujms.559796
Chicago Vergili, Tane, ve Ayse Borat. “Digital Lusternik-Schnirelmann Category of Digital Functions”. Hacettepe Journal of Mathematics and Statistics 49, sy. 4 (Ağustos 2020): 1414-22. https://doi.org/10.15672/hujms.559796.
EndNote Vergili T, Borat A (01 Ağustos 2020) Digital Lusternik-Schnirelmann category of digital functions. Hacettepe Journal of Mathematics and Statistics 49 4 1414–1422.
IEEE T. Vergili ve A. Borat, “Digital Lusternik-Schnirelmann category of digital functions”, Hacettepe Journal of Mathematics and Statistics, c. 49, sy. 4, ss. 1414–1422, 2020, doi: 10.15672/hujms.559796.
ISNAD Vergili, Tane - Borat, Ayse. “Digital Lusternik-Schnirelmann Category of Digital Functions”. Hacettepe Journal of Mathematics and Statistics 49/4 (Ağustos 2020), 1414-1422. https://doi.org/10.15672/hujms.559796.
JAMA Vergili T, Borat A. Digital Lusternik-Schnirelmann category of digital functions. Hacettepe Journal of Mathematics and Statistics. 2020;49:1414–1422.
MLA Vergili, Tane ve Ayse Borat. “Digital Lusternik-Schnirelmann Category of Digital Functions”. Hacettepe Journal of Mathematics and Statistics, c. 49, sy. 4, 2020, ss. 1414-22, doi:10.15672/hujms.559796.
Vancouver Vergili T, Borat A. Digital Lusternik-Schnirelmann category of digital functions. Hacettepe Journal of Mathematics and Statistics. 2020;49(4):1414-22.