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In this Book Chapter (invited) we briefly review the basic concepts defining topological insulators and focus on elaborating on the key experimental results that revealed and established their symmetry protected (SPT) topological nature. We…
In this note we investigate to what extent the fundamental group of a metric space can be described as the inverse limit of its discrete fundamental groups. We show that some mild conditions suffice to imply the existence of an isomorphism…
We suggest that trialgebraic symmetries migth be a sensible starting point for a notion of integrability for two dimensional spin systems. For a simple trialgebraic symmetry we give an explicit condition in terms of matrices which a…
In this paper, we consider certain topological properties along with certain types of mappings on these spaces defined by the notion of ideal convergence. In order to do that, we primarily follow in the footsteps of the earlier studies of…
In this paper, we introduce a Grothendieck topology on the category of totally bounded metric spaces and develop a theory of stacks with respect to this topology. We further define the fine moduli stack of compact metric spaces and prove…
We develop persistent homology in the setting of filtrations of (Cech) closure spaces. Examples of filtrations of closure spaces include metric spaces, weighted graphs, weighted directed graphs, and filtrations of topological spaces. We use…
Free actions of finite groups on spheres give rise to topological spherical space forms. The existence and classification problems for space forms have a long history in the geometry and topology of manifolds. In this article, we present a…
Closure spaces are a generalisation of topological spaces obtained by removing the idempotence requirement on the closure operator. We adapt the standard notion of bisimilarity for topological models, namely Topo-bisimilarity, to closure…
Injectivity of objects with respect to a set $\ch$ of morphisms is an important concept of algebra, model theory and homotopy theory. Here we study the logic of injectivity consequences of $\ch$, by which we understand morphisms $h$ such…
We consider perturbations of unitary minimal models by boundary fields. Initially we consider the models in the limit as c -> 1 and find that the relevant boundary fields all have simple interpretations in this limit. This interpretation…
Higher-order topological insulators are a recently discovered class of materials that can possess zero-dimensional localized states regardless of the dimension of the lattice. Here, we experimentally demonstrate that the topological…
In this paper we introduce the notion of interval valued hesitant fuzzy soft topological space. Also the concepts of interval valued hesitant fuzzy soft closure, interior and neighbourhood are introduced here and established some important…
We study the geometry of spaces of fitrations on a Noetherian local domain. We introduce a metric $d_1$ on the space of saturated filtrations, inspired by the Darvas metric in complex geometry, such that it is a geodesic metric space. In…
The main purpose of this paper is to investigate commuting flows and integrable systems on the configuration spaces of planar linkages. Our study leads to the definition of a natural volume form on each configuration space of planar…
We find universal spaces for Alexandroff and finite spaces and explore some of its topological properties as well as their description as inverse limits of finite spaces and Alexandroff extensions. They can be used as a natural environment…
Topology may be interpreted as the study of verifiability, where opens correspond to semi-decidable properties. In this paper we make a distinction between verifiable properties themselves and processes which carry out the verification…
Let $R$ be a commutative ring and $S \subseteq R$ be a multiplicative subset. We introduce and study the concept of $S$-purity based on the notion of $S$-strongly flat modules. The class of $S$-pure injective modules will be studied. We…
We investigate variations of Brieskorn lattices over non-compact parameter spaces, and discuss the corresponding limit objects on the boundary divisor. We study the associated variation of twistors and the corresponding limit mixed twistor…
A Cech closure space $(X,u)$ is a set $X$ with a (Cech) closure operator $u$ which need not be idempotent. Many properties which hold in topological spaces hold in Cech closure spaces as well. The notions of proper (splitting) and…
The main purpose of this paper is to introduce and study the primal-proximity spaces. Also, we define two new operators via primal proximity spaces and investigate some of their fundamental properties. In addition, we obtain a new topology,…