相关论文: Universal Coverings for Limit and Pseudotopologica…
We survey techniques for constructing spaces with non-trivial self covers. These processes include methods for building low and high dimension continua which non-trivially self. We also discuss several related group theoretic and…
Orbit-finite sets are a generalisation of finite sets, and as such support many operations allowed for finite sets, such as pairing, quotienting, or taking subsets. However, they do not support function spaces, i.e. if X and Y are…
The aim of this paper is to introduce the concepts of homotopical smallness and closeness. These are the properties of homotopical classes of maps that are related to recent developments in homotopy theory and to the construction of…
Topological conformal field theories are defined using only basic results from the theory of quasiconformal mappings.
Recently, Mr\v{s}evi\'{c} and Reilly discussed some covering properties of a topological space and its associated $\alpha$-topology in both topological and bitopological ways. The main aim of this paper is to investigate some common and…
Subspace codes are the $q$-analog of binary block codes in the Hamming metric. Here the codewords are vector spaces over a finite field. They have e.g. applications in random linear network coding, distributed storage, and cryptography. In…
This paper develops new tools for understanding surfaces with more than one end (and usually, of infinite topology) which properly minimally embed into Euclidean three-space. On such a surface, the set of ends forms a compact Hausdorff…
We give a characterization of limits of dihedral groups in the space of finitely generated marked groups. We also describe the topological closure of dihedral groups in the space of marked groups on a fixed number of generators.
In this paper I survey some recent results on finite determination, convergence, and approximation of formal mappings between real submanifolds in complex spaces. A number of conjectures are also given.
In various areas of modern physics and in particular in quantum gravity or foundational space-time physics it is of great importance to be in the possession of a systematic procedure by which a macroscopic or continuum limit can be…
We prove that an equivalent condition for a uniform space to be coverable is that the images of the natural projections in the fundamental inverse system are uniformly open in a certain sense. As corollaries we (1) obtain a concrete way to…
We prove some extension theorems involving uniformly continuous maps of the universal Urysohn space. We also prove reconstruction theorems for certain groups of autohomeomorphisms of this space and of its open subsets.
We consider shift spaces in which elements of the alphabet may overlap nontransitively. We define a notion of entropy for such spaces, give several techniques for computing lower bounds for it, and show that it is equal to a limit of…
The purpose of this paper is twofold. First, we define the new spaces and investigate some topological and structural properties. Also, we compute dual spaces of new spaces which are help us in the characterization of matrix mappings.…
Given a two--dimensional mapping $U$ whose components solve a divergence structure elliptic equation, we give necessary and sufficient conditions on the boundary so that $U$ is a global diffeomorphism.
The thesis presents the subject of synthetic topology, especially with relation to metric spaces. A model of synthetic topology is a categorical model in which objects possess an intrinsic topology in a suitable sense, and all morphisms are…
In this paper we develop some combinatorial models for continuous spaces. In this spirit we study the approximations of continuous spaces by graphs, molecular spaces and coordinate matrices. We define the dimension on a discrete space by…
In this paper, we are interested in study subgroups of topologized fundamental groups and their influences on generalized covering maps. More precisely, we find some relationships between generalized covering subgroups and the other famous…
In this paper, we define and prove basic properties of complement polyhedral product spaces, dual complexes and polyhedral join complexes. Then we compute the universal algebra of polyhedral join complexes under certain split conditions and…
The aim of this paper is twofold. Firstly, we give easy-to-handle criteria to determine whether a given family of subsets of a vector space is a neighbourhood basis of the origin for a complete vector topology. Then, we apply these criteria…