Related papers: On Completion of Metric Mappings
Multinets are certain configurations of lines and points with multiplicities in the complex projective plane $\mathbb{P}^2$. They appear in the study of resonance and characteristic varieties of complex hyperplane arrangement complements…
This paper is devoted to studying of some properties of multivalued mappings in Euclidean space. There were proved theorems on a fixed point for multivalued mappings whose restrictions to some subset in the closure of a domain satisfy "a…
The fixed-point theory and its applications to various areas of science are well known. In this paper we present some existence and uniqueness theorems for fixed circles of self-mappings on metric spaces with geometric interpretation. We…
We prove that any closed map between metrizable spaces can be extended to a closed map between completely metrizable spaces with the same extensional dimension.
The mapper construction is a powerful tool from topological data analysis that is designed for the analysis and visualization of multivariate data. In this paper, we investigate a method for stitching a pair of univariate mappers together…
In the present paper, we will study geometric properties of harmonic mappings whose analytic and co-analytic parts are (shifted) generated functions of completely monotone sequences.
This note presents an approach to studying the iterates of a mapping whose restriction to the complement of a finite set is continuous and open. The main examples to which the approach can be applied are piecewise monotone mappings defined…
Each complex network (or class of networks) presents specific topological features which characterize its connectivity and highly influence the dynamics of processes executed on the network. The analysis, discrimination, and synthesis of…
In the finite dimensional case, mean-type mappings, their invariant means, relations between the uniqueness of invariant means and convergence of orbits of the mapping, are considered. In particular it is shown, that the uniqueness of an…
We give an informal, expository account of a project to construct completions of period maps.
A good deal of current research in complex networks involves the characterization and/or classification of the topological properties of given structures, which has motivated several respective measurements. This letter proposes a framework…
A procedure to characterize chaotic dynamical systems with concepts of complex networks is pursued, in which a dynamical system is mapped onto a network. The nodes represent the regions of space visited by the system, while edges represent…
In many networks, including networks of protein-protein interactions, interdisciplinary collaboration networks, and semantic networks, connections are established between nodes with complementary rather than similar properties. While…
We determine the local geometric structure of two-dimensional metric spaces with curvature bounded above as the union of finitely many properly embedded/branched immersed Lipschitz disks. As a result, we obtain a graph structure of the…
Connectedness, path connectedness, and uniform connectedness are well-known concepts. In the traditional presentation of these concepts there is a substantial difference between connectedness and the other two notions, namely connectedness…
We study cross ratios from an axiomatic viewpoint, also known as the study of M\"obius spaces. We characterise cross ratios induced by quasi-metrics in terms of topological properties of their image. Furthermore, we generalise the notions…
In a separably connected space any two points are contained in a separable connected subset. We show a mechanism that takes a connected bounded metric space and produces a complete connected metric space whose separablewise components form…
The $\lambda$-perfect maps, a generalization of perfect maps (continuous closed maps with compact fibers) are presented. Using $P_\lambda$-spaces and the concept of $\lambda$-compactness some results regarding $\lambda$-perfect maps will be…
This article is devoted to the study of mappings with branch points whose characteristics satisfy integral-type constraints. We have proved theorems concerning their local and global behavior. In particular, we established the…
Finite metric spaces arise in many different contexts. Enormous bodies of data, scientific, commercial and others can often be viewed as large metric spaces. It turns out that the metric of graphs reveals a lot of interesting information.…