Related papers: Generalizing Topology via Chu Spaces

Various topological concepts are often involved in the research of mathematical logic, and almost all of these concepts can be regarded as developing from the Stone representation theorem. In the Stone representation theorem, a Boolean…

This paper considers generalised network, intended as networks where (a) the edges connecting the nodes are nonlinear, and (b) stochastic processes are continuously indexed over both vertices and edges. Such topological structures are…

In this work we present some new understanding of topological order, including three main aspects: (1) It was believed that classifying topological orders corresponds to classifying gapped quantum states. We show that such a statement is…

This book provides an introduction to the theory of digital (molecular) spaces (TDS). Digital spaces are combinatorial models of continuous spaces. TDS is one of alternative branches of digital topology that studies constructing and…

In many areas of applied geometric/numeric computational mathematics, including geo-mapping, computer vision, computer graphics, finite element analysis, medical imaging, geometric design, and solid modeling, one has to compute incidences,…

Predicting the future of Graph-supported Time Series (GTS) is a key challenge in many domains, such as climate monitoring, finance or neuroimaging. Yet it is a highly difficult problem as it requires to account jointly for time and graph…

The article is devoted to a structure of topological spaces related with topological quasigroups. Regular and complete spaces over topological quasigroups are studied. Separations and embeddings are also investigated for them. Their…

This paper concerns the self-similarity of topological spaces, in the sense defined in math.DS/0411344. I show how to recognize self-similar spaces, or more precisely, universal solutions of self-similarity systems. Examples include the…

In this lecture note, we give a basic introduction to the rapidly developing concepts of generalized symmetries, from the perspectives of both high energy physics and condensed matter physics. In particular, we emphasize on the (invertible)…

The communications and interrelations between different locations on the Earth's surface have far-reaching implications for both social and natural systems. Effective spatial analytics ideally require a spatial representation, where…

Consider a finite dimensional (generally reducible) polynomial representation \rho of GL_n. A projective compactification of GL_n is the closure of \rho(GL_n) in the space of all operators defined up to a factor (this class of spaces can be…

We present a set of principles and methodologies which may serve as foundations of a unifying theory of Mathematics. These principles are based on a new view of Grothendieck toposes as unifying spaces being able to act as `bridges' for…

A detailed study of graded frame, graded fuzzy topological system and fuzzy topological space with graded inclusion is already done in our earlier paper. The notions of graded fuzzy topological system and fuzzy topological space with graded…

We survey foundational principles of Grothendieck's generalized spaces, including a critical glossary of the various, and often conflicting, terminological usages. Known results using generalized points support a fully pointwise notation…

Geographic space is better understood through the topological relationship of the underlying streets (note: entire streets rather than street segments), which enables us to see scaling or fractal or living structure of far more…

We introduce the notion of functionally compact sets into the theory of nonlinear generalized functions in the sense of Colombeau. The motivation behind our construction is to transfer, as far as possible, properties enjoyed by standard…

We propose a generalization of small world networks, in which the reconnection of links is governed by a function that depends on the distance between the elements to be linked. An adequate choice of this function lets us control the…

We propose a definition of computable manifold by introducing computability as a structure that we impose to a given topological manifold, just in the same way as differentiability or piecewise linearity are defined for smooth and PL…

We discuss topological versions of the closed graph theorem, where continuity is inferred from near continuity in tandem with suitable conditions on source or target spaces. We seek internal characterizations of spaces satisfying a closed…

In this paper, we introduce and explore a new class of topological spaces termed as SC*-normal spaces, defined via SC*-open sets. The concept of SC*-normality is analyzed in relation to classical notions such as normal spaces and g-normal…