ON DIGITAL H-GROUPS

Year 2019, Volume: 2 Issue: 1, 42 - 50, 30.01.2019

Sibel Demiralp Essam Hamouda

https://doi.org/10.33773/jum.469626

Cited By: 1

Abstract

In this paper, specific properties of digital H-spaces and digital H-groups are studied. It is shown that there is a contravariant functor from the homotopy category of the pointed digital images to the category of groups and homomorphisms. Then it is proven that a pointed digital image having the same digital homotopy type as a digital H-group is itself a digital H-group.

Keywords

Digital image, digital homotopy, digital H-space, digital H-group

References

• R. Ayala, E. Dominguez, A. R. Francies, and A.Quintero, Homotopy in digital spaces. Discrete Applied Mathematics, 125(1), 3-24,(2003)
• L. Boxer, Digitally continuous functions, Pattern Recognition Letters 15.8, 833-839, (1994).
• L. Boxer, A classical construction for the digital fundamental group. Journal of Mathematical Imaging and Vision, 10(1), 51-62,(1999).
• L. Boxer, Properties of digital homotopy, Journal of Mathematical Imaging and Vision, 22(1), 19-26, (2005).
• O. Ege and I. Karaca, Digital H-spaces. In International Symposium on Computing in Science & Engineering. Proceedings . GEDIZ University, Engineering and Architecture Faculty. p. 133, (2013, January).
• O. Ege and I. Karaca, Banach fixed point theorem for digital images. J. Nonlinear Sci. Appl, 8(3), 237-245, (2015).
• O. Ege and I. Karaca, Some properties of digital H-spaces. Turkish Journal of Electrical Engineering \& Computer Sciences, 24(3), 1930-1941, (2016).
• S. E. Han, Non-product property of the digital fundamental group. Information Sciences 171(1-3), 73-91,(2005).
• S. E. Han, Remarks on digital homotopy equivalence. Honam Mathematical Journal, 29(1), 101-118, (2007).
• S. E. Han, KD-(k$_{0}$, k$_{1}$)-homotopy equivalence and its applications. Journal of the Korean Mathematical Society, 47(5), 1031-1054, (2010).
• T. Y. Kong, Roscoe, A. W. and Rosenfeld, A., Concepts of digital topology. Topology and its Applications, 46(3), 219-262, (1992).
• A. Mutlu, B. Mutlu and S. Oztunc, On Digital Homotopy of Digital Paths, International Research Journal of Pure Algebra 2(6), 147-154, (2012).
• S. Oztunc, and Mutlu, A. Categories in digital images. Am. J. Math. Stat, 3(1), 62-66, (2013).
• A. Rosenfeld, Digital topology, The American Mathematical Monthly, 86(8)621-630, (1979).
• R. M. Switzer, Algebraic topology-homotopy and homology, Springer. (2017).
• E. H. Spanier, Algebraic topology, Springer Science & Business Media 55(1) (1989).
• T. Yung Kong, A digital fundamental group, Computers & Graphics 13.2, 159-166,(1989)