相关论文: Continuity up to a Covering and Connectedness

Citation networks can reveal many important information regarding the development of science and the relationship between different areas of knowledge. Thus, many studies have analyzed the topological properties of such networks.…

The rules in a shape grammar apply in terms of embedding to take advantage of the parts that emerge visually in the appearance of shapes. While the shapes are kept unanalyzed as a computation moves forward, part-structures for shapes can be…

One major open problem in network coding is to characterize the capacity region of a general multi-source multi-demand network. There are some existing computational tools for bounding the capacity of general networks, but their…

Persistent homology provides a robust methodology to infer topological structures from point cloud data. Here we explore the persistent homology of point clouds embedded into a probabilistic setting, exploiting the theory of point…

Can the topology of a network that consists of many particles interacting with each other change in complexity when a phase transition occurs? The answer to this question is particularly interesting to understand the nature of phase…

General relativity does not allow one to specify the topology of space, leaving the possibility that space is multi-- rather than simply--connected. We review the main mathematical properties of multi--connected spaces, and the different…

The flourishing of topological photonics in the last decade was achieved mainly due to developments in linear topological photonic structures. However, when nonlinearity is introduced, many intriguing questions arise. For example, are there…

A topos theoretic generalisation of the category of sets allows for modelling spaces which vary according to time intervals. Persistent homology, or more generally, persistence is a central tool in topological data analysis, which examines…

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 investigate two approximation relations on a T0 topological space, the n-approximation, and the d-approximation, which are generalizations of the way-below relation on a dcpo. Different kinds of continuous spaces are defined by the two…

Basic pairs and their morphisms are the most elementary framework in which standard topological notions can be defined. We present here a new interpretation of topological concepts as those which can be communicated faithfully between the…

A connected covering is a design system in which the corresponding {\em block graph} is connected. The minimum size of such coverings are called {\em connected coverings numbers}. In this paper, we present various formulas and bounds for…

Spaces of quasi-invariant measures supplied with different topologies are studied. Their embeddings, projective decompositions, conditions for their metrizability are investigated. Theorems about convergence of nets of quasi-invariant…

Nestedness characterizes the linkage pattern of networked systems, indicating the likelihood that a node is linked to the nodes linked to the nodes with larger degrees than it. Networks of mutualistic relationship between distinct groups of…

Persistent homology is a topological data analysis tool that has been widely generalized, extending its scope beyond the field of topology. Among its extensions, steady and ranging persistence were developed to study a wide variety of graph…

Networked structures arise in a wide array of different contexts such as technological and transportation infrastructures, social phenomena, and biological systems. These highly interconnected systems have recently been the focus of a great…

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…

We investigate some properties of topological groups related to disconnectedness or Archimedeanness. We prove or disprove the preservation of those under operations as subgroups, quotients, products, etc. Characterizations of…

In this note we make use of some properties of vector fields on a manifold to give an alternate proof to [3] for the equivalence between connections and parallel transport on vector bundles over manifolds. Out of the proof will emerge a new…

By a fixed continuous map from a $3$-space to itself, a knot in the $3$-space may be mapped to another knot in the $3$-space. We analyze possible knot types of them. Then we map a knot repeatedly by a fixed continuous map and analyze…