Subsets and freezing sets in the digital plane

Year 2021, Volume: 50 Issue: 4, 991 - 1001, 06.08.2021

Laurence Boxer

https://doi.org/10.15672/hujms.827556

Cited By: 1

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 $(X,c_i)$ 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

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