相关论文: Topological dimension of a space is determined by …
In this paper we study the 2-dimension of a finite poset from the topological point of view. We use homotopy theory of finite topological spaces and the concept of a beat point to improve the classical results on 2-dimension, giving a more…
This article has been withdrawn due to an error in a proof of the main result.
In this paper we define a numerical shape invariant of a continuous map called shape dimension of a map, which generalizes the shape dimension of a topological space. Some basic properties and applications of this invariant are given. The…
A new methodological approach for the study of topology for shapes made of arrangements of lines, planes or solids is presented. Topologies for shapes are traditionally built on the classical theory of point-sets. In this paper, topologies…
In this paper, we prove that for a topological dynamical system with positive mean topological dimension and marker property, it has factors of arbitrary small mean topological dimension and zero relative mean topological dimension which…
For a finite partially ordered set we calculate the dimension of the variety of its subspace representations having fixed dimension vector. The dimension is given in terms of the Euler quadratic form associated with a partially ordered set,…
We argue that dimensionality is not absolute, but that it depends on the scale of resolution, from the Planck to the macro scale.
I withdraw the previous version of the paper since it contains conceptual and mathematical mistakes. I will soon replace it with a radically revised version.
It seems to be a common belief that the space in which we live is a space-time manifold of dimension at least four. In the present article we wish to draw attention to a slightly different possibility - a space-time pseudomanifold (or even…
Convergence theory is an extension of general topology. In contrast with topology, it is closed under some important operations, like exponentiation. With all its advantages, convergence theory remains rather unknown. It is an aim of this…
In this paper we consider two types of dimension that can be defined for products of one-dimensional topologically totally transcendental (t.t.t) structures. The first is topological and considers the interior of projections of the set onto…
This paper has been withdrawn by the author.
We show that, over a field of characteristic 0, a normal, projective variety of dimension at least 4 is uniquely determined by its underlying topological space. The proof builds on previous work of Lieblich and Olsson. Version 2: many small…
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…
Given a non-degenerate Peano continuum $X$, a dimension function $D:2^X_*\to[0,\infty]$ defined on the family $2^X_*$ of compact subsets of $X$, and a subset $\Gamma\subset[0,\infty)$, we recognize the topological structure of the system…
The goal of this article is to survey recent developments in the theory of contact structures in dimension three.
Gromov introduced two distance functions, the box distance and the observable distance, on the space of isomorphism classes of metric measure spaces and developed the convergence theory of metric measure spaces. We investigate several…
Real-valued triplet of scalar fields as source gives rise to a metric which tilts the scalar, not the light cone, in 2+1-dimensions. The topological metric is static, regular and it is characterized by an integer $\kappa =\pm 1,\pm 2,...$.…
According to a conjecture of Lindenstrauss and Tsukamoto, a topological system $(X,T)$ embeds in the $d$-dimensional cubical shift $(([0,1]^d)^\mathbb{Z},$shift) if its mean dimension and periodic dimension verify mdim$(X,T)<d/2$ and…
This paper has been withdrawn by the author. It will be replaced, substantially modified, by sections of the author's completed PhD thesis.