Multivalued Functions in Digital Topology

We study several types of multivalued functions in digital topology

Variants on Digital Covering Maps

SE Han's paper [11] discusses several variants of digital covering maps. We show several equivalences among these variants and discuss shortcomings in Han's paper

Convexity and freezing sets in digital topology

[EN] We continue the study of freezing sets in digital topology, introduced in [4]. We show how to find a minimal freezing set for a "thick" convex disk X in the digital plane Z^2. We give examples showing the significance of the assumption that X is convex.The suggestions and corrections of the anonymous reviewers are gratefully acknowledged.Boxer, L. (2021). Convexity and freezing sets in digital topology. Applied General Topology. 22(1):121-137. https://doi.org/10.4995/agt.2021.14185OJS121137221L. 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:1008370600456L. Boxer, Remarks on fixed point assertions in digital topology, 2, Applied General Topology 20, no. 1 (2019), 155-175. https://doi.org/10.4995/agt.2019.10667L. Boxer, Remarks on fixed point assertions in digital topology, 3, Applied General Topology 20, no. 2 (2019), 349-361. https://doi.org/10.4995/agt.2019.11117L. Boxer, Fixed point sets in digital topology, 2, Applied General Topology 21, no. 1 (2020), 111-133. https://doi.org/10.4995/agt.2020.12101L. Boxer, Remarks on fixed point assertions in digital topology, 4, Applied General Topology 21, no. 2 (2020), 265-284. https://doi.org/10.4995/agt.2020.13075L. Boxer, Approximate fixed point properties in digital topology, Bulletin of the International Mathematical Virtual Institute 10, no. 2 (2020), 357-367.L. Boxer, Approximate fixed point property for digital trees and products, Bulletin of the International Mathematical Virtual Institute 10, no. 3 (2020), 595-602.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.2016.4704L. Boxer and P.C. Staecker, Fixed point sets in digital topology, 1, Applied General Topology 21, no. 1 (2020), 87-110. https://doi.org/10.4995/agt.2020.12091L. Chen, Gradually varied surfaces and its optimal uniform approximation, SPIE Proceedings 2182 (1994), 300-307. https://doi.org/10.1117/12.171078L. Chen, Discrete Surfaces and Manifolds, Scientific Practical Computing, Rockville, MD, 2004.O. Ege and I. Karaca, Banach fixed point theorem for digital images, Journal of Nonlinear Sciences and Applications 8 (2015), 237u-245. https://doi.org/10.22436/jnsa.008.03.08J. Haarmann, M. . 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/s10851-015-0578-8A. Rosenfeld, Digital topology, The American Mathematical Monthly 86, no. 8 (1979), 621-630. https://doi.org/10.1080/00029890.1979.11994873A. Rosenfeld, 'Continuous' functions on digital pictures, Pattern Recognition Letters 4 (1986), 177-184. https://doi.org/10.1016/0167-8655(86)90017-

Remarks on digital deformation

The paper [5] defines a notion of digital deformation and claims to prove that if (X, p) is k-deformable into (A, p), then these two pointed images have isomorphic fundamental groups. We present a simple counterexample to this claim