30 citations · 48 across the 28 of their papers we have counts for
5 papers · 1 filter
Remarks on Fixed Point Assertions in Digital Topology, 5
Laurence Boxer
We discuss published assertions concerning fixed points in digital metric spaces that are incorrect or incorrectly proven, or reduce to triviality.
Beyond the Hausdorff Metric in Digital Topology
Laurence Boxer
Two objects may be close in the Hausdorff metric, yet have very different geometric and topological properties. We examine other methods of comparing digital images such that objec…
Hyperspaces and Function Graphs in Digital Topology
Laurence Boxer
We adapt the study of hyperspaces and function spaces from classical topology to digital topology. We define digital hyperspaces and digital function graphs, and study some of thei…
Cold and Freezing Sets in the Digital Plane
Laurence Boxer
Cold sets and freezing sets belong to the theory of (approximate) fixed points for continuous self-maps on digital images. We study some properties of cold sets for digital images…
AFPP and Unions of Convex Disks in the Digital Plane
Laurence Boxer
We use results of [6] to enlarge our knowledge of the approximate fixed point property (AFPP) for digital images in . In particular, we study conditions under which t…