30 citations · 48 across the 28 of their papers we have counts for
36 papers
Trimming and Building Freezing Sets
Laurence Boxer
We develop new tools for the construction of fixed point sets in digital topology. We define excludable points and show that these may be excluded from all freezing sets. We show t…
Remarks on Fixed Point Assertions in Digital Topology, 7
Laurence Boxer
This paper continues a series discussing flaws in published assertions concerning fixed points in digital images.
Limiting Sets for Digital Cones and Suspensions
Laurence Boxer
Cone and suspension constructions have been introduced in digital topology, modeled on those of classical topology. For digital cones and suspensions, and for some related digital…
Variants on Digital Covering Maps
Laurence Boxer
SE Han's paper [11] discusses several variants of digital covering maps. We show several equivalences among these variants and discuss shortcomings in Han's paper.
Limiting Sets in Digital Topology
Laurence Boxer
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 limit…
Remarks on Fixed Point Assertions in Digital Topology, 6
Laurence Boxer
This paper continues a series discussing flaws in published assertions concerning fixed points in digital metric spaces.
Freezing Sets for Arbitrary Digital Dimension
Laurence Boxer
We show how to obtain freezing sets for digital images in for arbitrary , using the and adjacencies.
Some Consequences of Restrictions on Digitally Continuous Functions
Laurence Boxer
We study the consequences of some restrictions on digitally continuous functions. One of our results modifies easily to yield an analogous result for topological spaces.
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…
Convexity and AFPP in the Digital Plane
Laurence Boxer
We examine the relationship between convexity and the approximate fixed point property (AFPP) for digital images in Z^2.
Subsets and Freezing Sets in the Digital Plane
Laurence Boxer
We continue the study of freezing sets for digital images introduced in [4, 2, 3]. We prove methods for obtaining freezing sets for digital images (X, c_i) for X \subset Z^2 and i…
Convexity and Freezing Sets in Digital Topology
Laurence Boxer
We continue the study of freezing sets in digital topology, introduced in [2]. We show how to find a minimal freezing set for a "thick" convex disk X in the digital plane Z^2. We g…
Approximate Fixed Point Property for Digital Trees and Products
Laurence Boxer
We add to our knowledge of the approximate fixed point property (AFPP) in digital topology. We show that a digital image that is a tree has the AFPP. Given two digital images (X, κ…
Remarks on Fixed Point Assertions in Digital Topology, 4
Laurence Boxer
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…
Approximate Fixed Point Properties in Digital Topology
Laurence Boxer
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 ab…
MSS_18 is Digitally 18-contractible
Laurence Boxer
The paper [10] incorrectly asserts that the digital image MSS_18, a digital model of the Euclidean 2-sphere S^2, is not 18-contractible. We show this assertion is false.
Fixed Point Sets in Digital Topology, 2
Laurence Boxer
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].…
Fixed point sets in digital topology, 1
Laurence Boxer, P. Christopher Staecker
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 cla…
Remarks on Fixed Point Assertions in Digital Topology, 3
Laurence Boxer
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…
Remarks on Fixed Point Assertions in Digital Topology, 2
Laurence Boxer
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 t…