Subsets and freezing sets in the digital plane

Authors : Laurence BOXER

Pages : 991-1001

Doi:10.15672/hujms.827556

View : 21 | Download : 9

Publication Date : 2021-08-06

Article Type : Research Paper

Abstract :We continue the study of freezing sets for digital images introduced in [L. Boxer and P.C. Staecker, Fixed point sets in digital topology, 1, Applied General Topology 2020; L. Boxer, Fixed point sets in digital topology, 2, Applied General Topology 2020; L. Boxer, Convexity and Freezing Sets in Digital Topology, Applied General Topology, 2021]. We prove methods for obtaining freezing sets for digital images $insert ignore into journalissuearticles values(X,c_i);$ for $X \subset \mathbb{Z}^2$ and $i \in \{1,2\}$. We give examples to show how these methods can lead to the determination of minimal freezing sets.
Keywords : digital topology, fixed point, freezing set, convex