Boxer, Laurence(Universitat Politècnica de València, 2022-04-01)
[EN] 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 objects close in each of these measures have ...
Herman, Gabor T.(Universitat Politècnica de València, 2007-04-01)
[EN] Intuitively, a boundary in an N-dimensional digital space is a connected component of the (N − 1)-dimensional surface of a connected object. In this paper we make these concepts precise, and show that the boundaries ...
Boxer, Laurence(Universitat Politècnica de València, 2021-04-01)
[EN] We continue the study of freezing sets in digital topology, introduced in [4]. We show how to find a minimal freezing set for a "thick" convex disk X in the digital plane Z^2. We give examples showing the significance of ...
[EN] 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 ...
Borat, Ayse(Universitat Politècnica de València, 2021-04-01)
[EN] In this paper, we define digital homotopic distance and give its relation with LS category of a digital function and of a digital image. Moreover, we introduce some properties of digital homotopic distance such as ...
Staecker, P. Christopher(Universitat Politècnica de València, 2021-10-01)
[EN] In this paper we prove results relating to two homotopy relations and four homology theories developed in the topology of digital images.We introduce a new type of homotopy relation for digitally continuous functions ...
Boxer, Laurence(Universitat Politècnica de València, 2020-04-03)
[EN] 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 ...
Boxer, Laurence; Staecker, P. Christopher(Universitat Politècnica de València, 2016-10-03)
[EN] The current paper focuses on fundamental groups and Euler characteristics of various digital models of the 2-dimensional sphere. For all models that we consider, we show that the fundamental groups are trivial, and ...
Boxer, Laurence(Universitat Politècnica de València, 2017-10-02)
[EN] We study properties of Cartesian products of digital images for which
adjacencies based on the normal product adjacency are used. We show
that the use of such adjacencies lets us obtain many "product properties"
for ...
Boxer, Laurence; Staecker, P. Christopher(Universitat Politècnica de València, 2019-04-01)
[EN] 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 ...
Boxer, Laurence(Universitat Politècnica de València, 2019-04-01)
[EN] 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 ...
Boxer, Laurence(Universitat Politècnica de València, 2019-10-01)
[EN] 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; ...
Boxer, Laurence(Universitat Politècnica de València, 2020-10-01)
[EN] 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.
Boxer, Laurence(Universitat Politècnica de València, 2022-10-03)
[EN] As in [6, 3, 4, 5], we discuss published assertions concerning fixed points in digital metric spaces - assertions that are incorrect or incorrectly proven, or reduce to triviality.
İs, Melih; Karaca, İsmet(Universitat Politècnica de València, 2020-10-01)
[EN] Y. Rudyak develops the concept of the topological complexity TC(X) defined by M. Farber. We study this notion in digital images by using the fundamental properties of the digital homotopy. These properties can also ...