Fixed point sets in digital topology, 2
Keywords:digital topology, digital image, fixed point, reducible image, retract, wedge, tree
AbstractWe continue the work of , studying properties of digital images determined by fixed point invariants. We introduce pointed versions of invariants that were introduced in . We introduce freezing sets and cold sets to show how the existence of a fixed point set for a continuous self-map restricts the map on the complement of the fixed point set.
C. Berge, Graphs and Hypergraphs, 2nd edition, North-Holland, Amsterdam, 1976.
L. Boxer, Digitally Continuous functions, Pattern Recognition Letters 15 (1994), 833-839. 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, Generalized normal product adjacency in digital topology, Applied General Topology 18, no. 2 (2017), 401-427. https://doi.org/10.4995/agt.2017.7798
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
L. Boxer, Fixed points and freezing sets in digital topology, Proceedings, Interdisciplinary Colloquium in Topology and its Applications in Vigo, Spain; 55-61.
L. Boxer, O. Ege, I. Karaca, J. Lopez and J. Louwsma, Digital fixed points, approximate fixed points, and universal functions, Applied General Topology 17, no. 2 (2016), 159-172. https://doi.org/10.4995/agt.2016.4704
L. Boxer and I. Karaca, Fundamental groups for digital products, Advances and Applications in Mathematical Sciences 11, no. 4 (2012), 161-180.
L. Boxer and P. C. Staecker, Fundamental groups and Euler characteristics of sphere-like digital images, Applied General Topology 17, no. 2 (2016), 139-158. https://doi.org/10.4995/agt.2016.4624
L. Boxer and P. C. Staecker, Fixed point sets in digital topology, 1, Applied General Topology, to appear.
G. Chartrand and L. Lesniak, Graphs & Digraphs, 2nd ed., Wadsworth, Inc., Belmont, CA, 1986.
J. Haarmann, M. P. Murphy, C. S. Peters and P. C. Staecker, Homotopy equivalence in finite digital images, Journal of Mathematical Imaging and Vision 53 (2015), 288-302. https://doi.org/10.1007/s10851-015-0578-8
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
E. Khalimsky, Motion, deformation, and homotopy in finite spaces, in Proceedings IEEE Intl. Conf. on Systems, Man, and Cybernetics, 1987, 227-234.
A. Rosenfeld, Digital topology, The American Mathematical Monthly 86, no. 8 (1979), 621-630. https://doi.org/10.1080/00029890.1979.11994873
A. Rosenfeld, 'Continuous' functions on digital pictures, Pattern Recognition Letters 4 (1986), 177-184. https://doi.org/10.1016/0167-8655(86)90017-6
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