Ayşe BORAT, Tane VERGİLİ

Digital Lusternik–Schnirelmann category

In this paper, we define the digital Lusternik–Schnirelmann category catκ , introduce some of its properties,and discuss how the adjacency relation affects the digital Lusternik–Schnirelmann category

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Boxer L. Digitally continuous functions. Pattern Recogn Lett 1994; 15: 833-839.
Boxer L. A classical construction for the digital fundamental group. J Math Imaging Vis 1999; 10: 51-62.
Boxer L. Properties of digital homotopy. J Math Imaging Vis 2005; 22: 19-26.
Boxer L. Homotopy properties of sphere-like digital images. J Math Imaging Vis 2006; 24: 167-175.
Boxer L. Continuous maps on digital simple closed curves. Springer P Math Stat 2010; 1: 377-386.
Boxer L, Karaca I. The Classification of digital covering spaces. J Math Imaging Vis 2008; 32: 23-29.
Boxer L, Staecker PC. Fundamental groups and Euler characteristics of sphere-like digital images. Appl Gen Topol 2016; 17: 139-158.
Cornea O, Lupton G, Oprea J, Tanre D. Lusternik-Schnirelmann category. Mathematical Surveys and Monographs, Vol. 103, Amer Math Soc 2003.
Han SE. On the classification of the digital images up to digital homotopy equivalence. J Comput Commun Res 2000; 10: 207-216.
Han SE. Computer topology and its applications. Honam Math J 2003; 25: 153-162.
Han SE. Non-product property of the digital k-fundamental group. Inform Sciences 2005; 173: 73-91.
Han SE. Digital fundamental group and Euler characteristic of a connected sum of digital closed surfaces. Inform Sciences 2007; 177: 3314-3326.
Han SE. A generalized digital (k0, k1)-homeomorphism. Note di Matematica 2003; 22: 157-166.
Herman GT. Oriented surfaces in digital spaces CVGIP. Graph Model Im Proc 1993; 55: 381-396.
Khalimsky E. Motion, deformation, and homotopy in finite spaces. Proceedings IEEE International Conference on Systems, Man, and Cybernetics 1987; 227-234.
Oztunc S. Morphism properties of digital categories. Celal Bayar University Journal of Science 2017; 13: 619-622.
Oztunc S, Bildik N, Mutlu A. The construction of simplicial groups in digital images. J Inequal Appl 2013; 143: 1-13.
Oztunc S, Mutlu A. Categories in digital images. Am J Math Stat 2013; 3: 62-66.
Oztunc S, Mutlu A, Bildik N. Computing hypercrossed complex pairings in digital images. Abstr Appl Anal 2013; 2013: 1-6.
Rosenfeld A. Continuous functions on digital pictures. Pattern Recogn Lett 1986; 4: 177-184.