Related papers: Remarks on Fixed Point Assertions in Digital Topol…

This paper continues a series discussing flaws in published assertions concerning fixed points in digital images.

This paper continues a series discussing flaws in published assertions concerning fixed points in digital metric spaces.

The topic of fixed points in digital metric spaces continues to draw publications with assertions that are incorrect, incorrectly proven, trivial, or incoherently stated. We continue the work of our earlier papers that discuss publications…

We continue the work of [5] and [3], in which are considered papers in the literature that discuss fixed point assertions in digital topology. We discuss published assertions that are incorrect or incorrectly proven; that are severely…

The topic of fixed points in digital metric spaces has drawn yet more publications with assertions that are incorrect, incorrectly proven, trivial, or incoherently stated. We discuss publications with bad assertions concerning fixed points…

We continue a discussion of published assertions that are incorrect, incorrectly proven, or trivial, in the theory of fixed points in digital topology.

We discuss published assertions concerning fixed points in digital metric spaces that are incorrect or incorrectly proven, or reduce to triviality.

We continue the work of [4, 2, 3], in which we discuss published assertions that are incorrect or incorrectly proven; that are severely limited or reduce to triviality; or that we improve upon.

Several recent papers in digital topology have sought to obtain fixed point results by mimicking the use of tools from classical topology, such as complete metric spaces and homotopy invariant fixed point theory. We show that in many cases,…

Several recent papers in digital topology have sought to obtain fixed point results by mimicking the use of tools from classical topology, such as complete metric spaces. We show that in many cases, researchers using these tools have…

We continue the work of [10], studying properties of digital images determined by fixed point invariants. We introduce pointed versions of invariants that were introduced in [10]. We introduce freezing sets and cold sets to show how the…

In this paper, we examine some properties of the fixed point set of a digitally continuous function. The digital setting requires new methods that are not analogous to those of classical topological fixed point theory, and we obtain results…

We study the approximate fixed point property (AFPP) for continuous single-valued functions and for continuous multivalued functions in digital topology. We extend what is known about these notions and discuss errors that have appeared in…

In this article, we investigate some properties of the coincidence point set of digitally continuous maps. Following the Rosenfeld graphical model which seems more combinatorial than topological, we expect to achieve results that might not…

The topology of digital images has been studied much in recent years, but no attempt has been made to exhaustively catalog the structure of binary images of small numbers of points. We produce enumerations of several classes of digital…

Freezing sets and cold sets have been introduced as part of the theory of fixed points in digital topology. In this paper, we introduce a generalization of these notions, the limiting set, and examine properties of limiting sets.

We give a quick survey of the various fixed point theorems in computability theory, partial combinatory algebra, and the theory of numberings, as well as generalizations based on those. We also point out several open problems connected to…

We study properties of Cartesian products of digital images, using a variety of adjacencies that have appeared in the literature.

S.E. Hans paper, Remarks on Pseudocovering Spaces in a Digital Topological Setting: A Corrigendum, is meant to address errors in previous papers. However, this paper is also marked by errors in its mathematics, as well as improprieties in…

A. Rosenfeld introduced the notion of a digitally continuous function between digital images, and showed that although digital images need not have fixed point properties analogous to those of the Euclidean spaces modeled by the images,…