Digital homotopic distance between digital functions

Ayse Borat

doi:10.4995/agt.2021.14542

Authors

Ayse Borat Bursa Technical University https://orcid.org/0000-0002-5628-7798

DOI:

https://doi.org/10.4995/agt.2021.14542

Keywords:

homotopic distance, Lusternik Schnirelmann category, digital topology

Abstract

In this paper, we define digital homotopic distance and give its relation with LS category of a digital function and of a digital image. Moreover, we introduce some properties of digital homotopic distance such as being digitally homotopy invariance.

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Author Biography

Ayse Borat, Bursa Technical University

Faculty of Engineering and Natural Scieces

Department of Mathematics

References

C. Berge, Graphs and Hypergraphs, 2nd edition, North-Holland, Amsterdam, 1976.

A. Borat and T. Vergili, Digital Lusternik-Schnirelmann category, Turkish Journal of Mathematics 42, no 1 (2018), 1845-1852. https://doi.org/10.3906/mat-1801-94

A. Borat and T. Vergili, Higher homotopic distance, Topological Methods in Nonlinear Analysis, to appear.

L. Boxer, Digitally continuous functions, Pattern Recognit. Lett. 15 (1994), 883-839. https://doi.org/10.1016/0167-8655(94)90012-4

L. Boxer, A classical construction for the digital fundamental group, Journal of Mathematical Imaging and Vision 10 (1999), 51-62. https://doi.org/10.1023/A:1008370600456

L. Boxer, Homotopy properties of sphere-like digital images, J. Math. Imaging Vision, 24 (2006), 167-175. https://doi.org/10.1007/s10851-005-3619-x

L. Boxer, Alternate product adjacencies in digital topology, Applied General Topology 19, no. 1 (2018), 21-53. https://doi.org/10.4995/agt.2018.7146

O. Cornea, G. Lupton, J. Oprea and D. Tanre, Lusternik-Schnirelmann Category, Mathematical Surveys and Monographs, vol. 103, American Mathematical Society 2003. https://doi.org/10.1090/surv/103

M. Farber, Topological complexity of motion planning, Discrete and Computational Geometry 29 (2003), 211-221. https://doi.org/10.1007/s00454-002-0760-9

S. E. Han, Non-product property of the digital fundamental group, Information Sciences 171 (2005), 73-91. https://doi.org/10.1016/j.ins.2004.03.018

M. Is and I. Karaca, The higher topological complexity in digital images, Applied General Topology 21, no. 2 (2020), 305-325. https://doi.org/10.4995/agt.2020.13553

I. Karaca and M. Is, Digital topological complexity numbers, Turkish Journal of Mathematics 42, no. 6 (2018), 3173-3181. https://doi.org/10.3906/mat-1807-101

E. Khalimsky, Motion, deformation, and homotopy in finite spaces, Proceedings IEEE International Conference on Systems, Man, and Cybernetics (1987), 227-234.

G. Lupton, J. Oprea and N. A. Scoville, Homotopy theory in digital topology, ArXiv: 1905.07783.

G. Lupton, J. Oprea and N. A. Scoville, Subdivisions of maps of digital images, ArXiv: 1906.03170.

E. Macias-Virgos and D. Mosquera-Lois, Homotopic distance between maps, Math. Proc. Cambridge Philos. Soc., to appear.

G. Sabidussi, Graph multiplication, Math. Z. 72 (1960), 446-457. https://doi.org/10.1007/BF01162967

T. Vergili and A. Borat, Digital Lusternik-Schnirelmann category of digital functions, Hacettepe Journal of Mathematics and Statistics 49, no. 4 (2020), 1414-1422. https://doi.org/10.15672/hujms.559796