相关论文: 2-Dimension from the topological viewpoint

Persistent Topology studies topological features of shapes by analyzing the lower level sets of suitable functions, called filtering functions, and encoding the arising information in a parameterized version of the Betti numbers, i.e. the…

Covering-based rough set theory is an extension to classical rough set. The main purpose of this paper is to study covering rough sets from a topological point of view. The relationship among upper approximations based on topological spaces…

In this paper we study the structure of complex points of codimension 2 real submanifolds in complex $n$ dimensional manifolds. We show that the local structure of a complex point up to isotopy only depends on their type (either elliptic or…

We consider the dimensions of finite type of representations of a partially ordered set, i.e. such that there is only finitely many isomorphism classes of representations of this dimension. We give a criterion for a dimension to be of…

The goal of Point Distance Solving Problems is to find 2D or 3D placements of points knowing distances between some pairs of points. The common guideline is to solve them by a numerical iterative method (\emph{e.g.} Newton-Raphson method).…

This paper presents a discrete homotopy theory and a discrete homology theory for finite posets. In particular, the discrete and classical homotopy groups of finite posets are always isomorphic. Moreover, this discrete homology theory is…

We show that Euclidean geometry in suitably high dimension can be expressed as a theory of orthogonality of subspaces with fixed dimensions and fixed dimension of their meet.

The fundamental bigroupoid of a topological space is one way of capturing its homotopy 2-type. When the space is semilocally 2-connected, one can lift the construction to a bigroupoid internal to the category of topological spaces, as Brown…

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…

Given a symmetric monoidal category $C$ with product $\sqcup$, where the neutral element for the product is an initial object, we consider the poset of $\sqcup$-complemented subobjects of a given object $X$. When this poset has finite…

In this paper we give a characterization of 2-dimensional topological field theories over a space $X$ as Frobenius bundles with connections over $LX$, the free loop space of $X$. This is a generalization of the folk theorem stating that…

In architecture, city planning, visual arts, and other design areas, shapes are often made with points, or with structural representations based on point-sets. Shapes made with points can be understood more generally as finite arrangements…

Several recent papers in digital topology have sought to obtain fixed point results by mimicking the use of tools from classical topology, such as complete metric spaces. We show that in many cases, researchers using these tools have…

This survey/expository article covers a variety of topics related to the "topology at infinity" of noncompact manifolds and complexes. In manifold topology and geometric group theory, the most important noncompact spaces are often…

As a continuation of \cite{NSY:local}, we mainly discuss the global structure of two-dimensional locally compact geodesically complete metric spaces with curvature bounded above. We first obtain the result on the Lipschitz homotopy…

In this paper we study the number of finite topologies on an $n$-element set subject to various restrictions.

This work serves as an opening and basis of an ongoing program investigating topological and geometric aspects of the moduli space of smooth fiberings on a manifold. The present paper focuses on the algebraic and differential topology of…

Real data is often given as a point cloud, i.e. a finite set of points with pairwise distances between them. An important problem is to detect the topological shape of data --- for example, to approximate a point cloud by a low-dimensional…

We introduce several homotopy equivalence relations for proper holomorphic mappings between balls. We provide examples showing that the degree of a rational proper mapping between balls (in positive codimension) is not a homotopy invariant.…

Our main aim in this paper is to introduce a general concept of multidimensional fixed point of a mapping in spaces with distance and establish various multidimensional fixed point results. This new concept simplifies the similar notion…