Recent interest in topological semimetals has led to the proposal of many new topological phases that can be realized in real materials. Next to Dirac and Weyl systems, these include more exotic phases based on manifold band degeneracies in the bulk electronic structure. The exotic states in topological semimetals are usually protected by some sort of crystal symmetry, and the introduction of m...

Topological relationships between objects in space are of great importance in many disciplines. Due to the lack of local topological information between components, i.e. faces, in the model of topological relationships between complex regions, recently, localized topological relationships have been defined for complex regions based on the relationships between simple regions with holes. However...

This article is divided into two parts. In the first part, we prove some useful theorems on finite topological spaces. In the second part, in order to consider a family of neighborhoods to a point in a space, we extend the notion of finite topological space and define a new topological space, which we call formal topological space. We show the relation between formal topological space struct (F...

Serre [Se 64] and Abelson [Ab 74] have produced examples of conjugate algebraic varieties which are not homeomorphic. We show that if the field of definition of a polarized projective variety coincides with its field of moduli then all of its conjugates have the same topological type. This immediately extends the class of varietie s known to possess invariant topological type to all canonically...

We study the interplay between network topology and complex space-time patterns and introduce a concept to analytically predict complex patterns in networks of Stuart-Landau oscillators with linear symmetric and instantaneous coupling based solely on the network topology. These patterns consist of partial amplitude death and partial synchronization and are found to exist in large variety for al...

The notion of contra continuous functions was introduced and investigated by Dontchev. In this paper, we apply the notion of $beta^{*}$-closed sets in topological space to present and study a new class of functions called contra $beta^{*}$-continuous and almost contra $beta^{*}$-continuous functions as a new generalization of contra continuity.

This paper presents an integrated study on possible topological relationship between multidimensional simple objects in 0,1,2 and 3 D space. The formal categorisation of spatial relationships is completed upon the 9intersections model. The focus is on the definition of a unified set of conditions for eliminating relationships that cannot be realised in reality. The negative conditions are formu...

Spatial representations are useful in computer vision, graphics, Geographic Information Systems (GIS’s), diagrammatic reasoning, and robot motion planning, to name a few. The representations may be geometric, topological, statistical and symbolic in nature. Depending on the domain and the application, there are a wide variety of methods available to represent space and perform computations and ...

Recursive domain equations have natural solutions. In particular there are domains defined by strictly positive induction. The class of countably based domains gives a computability theory for possibly non-countably based topological spaces. A qcb0 space is a topological space characterized by its strong representability over domains. In this paper, we study strictly positive inductive definiti...

The additivity number of a topological property (relative to a given space) is the minimal number of subspaces with this property whose union does not have the property. The most well-known case is where this number is greater than א0, i.e. the property is σ-additive. We give a rather complete survey of the known results about the additivity numbers of a variety of topological covering properti...