Related papers: Which Topologies induced by order convergences
We study clustering properties of networks of single integrator nodes over a directed graph, in which the nodes converge to steady-state values. These values define clustering groups of nodes, which depend on interaction topology, edge…
Each finite algebra $\mathbf A$ induces a lattice~$\mathbf L_{\mathbf A}$ via the quasi-order~$\to$ on the finite members of the variety generated by~$\mathbf A$, where $\mathbf B \to \mathbf C$ if there exists a homomorphism from $\mathbf…
Topological phases of matter provide a flexible platform to engineer unconventional quantum excitations in quantum materials. Beyond single particle topological matter, in systems with strong quantum many-body correlations, many-body…
We prove some injectivity theorems. Our proof depends on the theory of mixed Hodge structures on cohomology groups with compact support. Our injectivity theorems would play crucial roles in the minimal model theory for higher-dimensional…
In this work, we will show how the topological order of the Toric Code appears when the lattice on which it is defined discretizes a three-dimensional torus. In order to do this, we will present a pedagogical review of the traditional…
We examine the topological characteristic cohomology classes of complexified vector bundles. In particular, all the classes coming from the real vector bundles underlying the complexification are determined.
The concept of coreflexive set is introduced to study the structure of digraphs. New characterizations of line digraphs and nth-order line digraphs are given. Coreflexive sets also lead to another natural way of forming an intersection…
We give characterizations of unital uniform topological algebras and saturated locally multiplicatively convex algebras by means of multiplicative linear functionals. Some automatic continuity theorems in advertibly complete uniform…
We involve a certain propositional logic based on ortholattices. We characterize the implicational reduct of such a logic and we show that its algebraic counterpart is the so-called orthosemilattice. Properties of congruences and congruence…
We show how to use topological ideas, such as compactness, to establish orderability properties of infinite groups. A new application is to provide a left-ordering for the group of PL homeomorphisms of a connected surface with boundary…
We define and study hierarchies of topological spaces induced by the classical Borel and Luzin hierarchies of sets. Our hierarchies are divided into two classes: hierarchies of countably based spaces induced by their embeddings into the…
A new and extensive formalism is developed for monads and galaxies in non-standard enlargements. It is shown that monads and galaxies can be manipulated using order-preserving and order-reversing set-to-set maps, and that set properties…
We define and study structural properties of hypergraphs of models of a theory including lattice ones. Characterizations for the lattice properties of hypergraphs of models of a theory, as well as for structures on sets of isomorphism types…
Cylindrical interfaces occur in sheared or deformed emulsions and as biological or technological lipid monolayer or bilayer tubules. Like the corresponding spherical droplets and vesicles, these cylinder-like surfaces may host orientaional…
The theory of pattern formation in reaction-diffusion systems is extended to the case of a directed network. Due to the structure of the network Laplacian of the scrutinised system, the dispersion relation has both real and imaginary parts,…
One of the ways that connectedness has been studied through the history of topology is by using chains, the so called chain connectedness. Here we combine this notion together with continuity up to a covering to provide the inheritance of…
This paper is devoted to the study of induced topological pressure, including both classical and nonlinear cases. For the classical induced topological pressure, we investigate equilibrium states, subdifferential and freezing states, while…
Link prediction in graphs is a task that has been widely investigated. It has been applied in various domains such as knowledge graph completion, content/item recommendation, social network recommendations and so on. The initial focus of…
We provide a process on the space of coalescing cadlag stable paths and show convergence in the appropriate topology for coalescing stable random walks on the integer lattice.
Trees of finite cone type have appeared in various contexts. In particular, they come up as simplified models of regular tessellations of the hyperbolic plane. The spectral theory of the associated Laplacians can thus be seen as induced by…