Related papers: Fractal Topology Foundations
Given strong local Dirichlet forms and $\mathbb{R}^N$-valued functions on a metrizable space, we introduce the concepts of geodesic distance and intrinsic distance on the basis of these objects. They are defined in a geometric and an…
We prove that every Peano continuum with uncountably many local cut points is a topological fractal. This extends some recent results and it partially answers a conjecture by Hata. We also discuss the number of mappings which are necessary…
We formulate a construction of type-I fracton models based on gauging planar subsystem symmetries of topologically ordered two dimensional layers that have been stacked in three ambient spatial dimensions. Via our construction, any defect…
Framed combinatorial topology is a novel theory describing combinatorial phenomena arising at the intersection of stratified topology, singularity theory, and higher algebra. The theory synthesizes elements of classical combinatorial…
Spacetime is represented by ordered sequences of topologically closed Poincare sections of the primary space constructed of primary empty cells. These mappings are constrained to provide homeomorphic structures serving as frames of…
Fracton models, a collection of exotic gapped lattice Hamiltonians recently discovered in three spatial dimensions, contain some 'topological' features: they support fractional bulk excitations (dubbed fractons), and a ground state…
Fracton topological order hosts fractionalized point-like excitations (e.g., fractons) that have restricted mobility. In this article, we explore even more bizarre realization of fracton phases that admit spatially extended excitations with…
The term fractal describes a class of complex structures exhibiting self-similarity across different scales. Fractal patterns can be created by using various techniques such as finite subdivision rules and iterated function systems. In this…
In this work, major principles of the mathematical constitution of space and the principles of construction of the physical space are presented. Generalized conceptions of distances and dimensionality evaluation are proposed, together with…
Observations of galaxies over large distances reveal the possibility of a fractal distribution of their positions. The source of fractal behavior is the lack of a length scale in the two body gravitational interaction. However, even with…
In [1] we introduced the concept of structured space, which is a topological space that locally resembles some algebraic structures. In [2] we proceeded the study of these spaces, developing two cohomology theories. The aim of this paper is…
This survey aims to provide a guide to the literature on topological 4-manifolds. Foundational theorems on 4-manifolds are stated, especially in the topological category. Precise references are given, with indications of the strategies…
In this paper we study self-similar and fractal networks from the combinatorial perspective. We establish analogues of topological (Lebesgue) and fractal (Hausdorff) dimensions for graphs and demonstrate that they are naturally related to…
The concept of derivative coordinate functions proved useful in the formulation of analytic fractal functions to represent smooth symmetric binary fractal trees [1]. In this paper we introduce a new geometry that defines the fractal space…
In this paper, we will investigate how radiality occurs in topological spaces by considering neighbourhood bases generated by nests. We will define a new subclass of radial spaces, called the independently-based spaces, that contains LOTS,…
The cosmic web structure is studied with the concepts and methods of fractal geometry, employing the adhesion model of cosmological dynamics as a basic reference. The structures of matter clusters and cosmic voids in cosmological N-body…
The functional features of spatial networks depend upon a non-trivial relationship between the topological and physical structure. Here, we explore that relationship for spatial networks with radial symmetry and disordered fractal…
The concept of quasi-partial b-metric-like spaces is being introduced and studied with the help of topology. Examples are also discussed to support the results. Some fixed point theorems are proved in the setting of quasi-partial…
The impact of inhomogeneous arrangement of nodes in space on network organization cannot be neglected in most of real-world scale-free networks. Here, we wish to suggest a model for a geographical network with nodes embedded in a fractal…
We provide a new perspective on fracton topological phases, a class of three-dimensional topologically ordered phases with unconventional fractionalized excitations that are either completely immobile or only mobile along particular lines…