Related papers: Pseudocovering and digital covering spaces
The present paper focuses on the notions of covering spaces, pseudo-covering spaces, and their equivalences. We discuss something incorrectly mentioned in Boxer's papers and correct them. Indeed, Sections 4-6 (or 4-6) of \cite{B3} are…
In this paper, by reviewing the concept of subcovering and semicovering maps, we extend the notion of subcovering map to subsemicovering map. We present some necessary or sufficient conditions for a local homeomorphism to be a…
The present paper refers to the notions of digital continuity, digital $k$-isomorphism, local $k$-isomorphism, radius $2$-local $k$-isomorphism, and digital $k$-homotopy motivated by the Khalimsky's version. We discuss something incorrectly…
In this study, we improve the topological complexity computations on digital images with introducing the digital topological complexity computations of a surjective and digitally continuous map between digital images. We also reveal…
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…
With a view towards providing tools for analyzing and understanding digitized images, various notions from algebraic topology have been introduced into the setting of digital topology. In the ordinary topological setting, invariants such as…
With the recent advancements in the field of information industry, critical data in the form of digital images is best understood by the human brain. Therefore, digital images play a significant part and backbone role in many areas such as…
Discrete cubical homology arose as the homology theory associated with discrete cubical homotopy theory. Despite the combinatorial nature of this homology, its computation has posed a significant challenge to the researchers in the field.…
In this article, we investigate properties of digital H-spaces in the graph theoretic model of digital topology. As in prior work, the results obtained often depend fundamentally on the choice between NP$_1$ and NP$_2$ product adjacencies.…
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.
Object: Modern computational MRI denoising approaches are often designed assuming fixed k-space coverage. This contrasts with earlier acquisition-design literature that leveraged k-space coverage modifications (e.g., reducing spatial…
In this paper we compare the concepts of pseudoradial spaces and the recently defined strongly pseudoradial spaces in the realm of compact spaces. We show that $\mathrm{MA}+\mathfrak{c}=\omega_2$ implies that there is a compact pseudoradial…
In this paper we show that a digital $(\kappa,\lambda)-$continuous surjection $p:(E,\kappa)\rightarrow (B,\lambda)$ is a digital covering map if and only if it is a local isomorphism. Moreover, we find a loop criterion for a digital…
Copy-move forgery is a manipulation of copying and pasting specific patches from and to an image, with potentially illegal or unethical uses. Recent advances in the forensic methods for copy-move forgery have shown increasing success in…
In this paper we devote to spaces that are not homotopically hausdorff and study their covering spaces. We introduce the notion of small covering and prove that every small covering of $X$ is the universal covering in categorical sense.…
There are three types of hypersurfaces in a pseudoconformal space C^n_1 of Lorentzian signature: spacelike, timelike, and lightlike. These three types of hypersurfaces are considered in parallel. Spacelike hypersurfaces are endowed with a…
The remarkable generative capabilities of denoising diffusion models have raised new concerns regarding the authenticity of the images we see every day on the Internet. However, the vast majority of existing deepfake detection models are…
The paper studies the deformation theory of a holomorphic surjective map from a normal compact complex space to a compact Kaehler manifold and describes the component of the space of holomorphic maps, generalizing results in the projective…
Digital topology has its own working conditions and sometimes differs from the normal topology. In the area of topological robotics, we have important counterexamples in this study to emphasize this red line between a digital image and a…
Using digital topology approach, we construct digital models of closed surfaces as the intersection graphs of LCL covers of the surfaces. It is proved that digital models of closed surfaces are digital 2-dimensional surfaces preserving the…