Convexity and freezing sets in digital topology

Laurence Boxer

Abstract

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.


Keywords

digital topology; freezing set; convexity; digital disk

Subject classification

54H25.

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References

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, Remarks on fixed point assertions in digital topology, 2, Applied General Topology 20, no. 1 (2019), 155-175. https://doi.org/10.4995/agt.2019.10667

L. 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.2019.11117

L. Boxer, Fixed point sets in digital topology, 2, Applied General Topology 21, no. 1 (2020), 111-133. https://doi.org/10.4995/agt.2020.12101

L. 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.2020.13075

L. 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.2016.4704

L. 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.2020.12091

L. Chen, Gradually varied surfaces and its optimal uniform approximation, SPIE Proceedings 2182 (1994), 300-307. https://doi.org/10.1117/12.171078

L. 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.008.03.08

J. 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/s10851-015-0578-8

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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1. Approximate Fixed Point Property and Unions of Convex Disks in the Digital Plane
Laurence Boxer
Topology and its Applications  first page: 107850  year: 2021  
doi: 10.1016/j.topol.2021.107850



Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt