相关论文: Problems from Topology Proceedings
In recent years, graph theory has been widely employed to probe several language properties. More specifically, the so-called word adjacency model has been proven useful for tackling several practical problems, especially those relying on…
A new edition of Walter K. Hayman's 'Research Problems in Function Theory' (1967), containing over five hundred function theory and complex analysis problems, along with all progress updates over the last 51 years. The final publication…
This monograph introduces key concepts and problems in the new research area of Periodic Geometry and Topology for materials applications.Periodic structures such as solid crystalline materials or textiles were previously classified in…
A series of recent papers by Bergfalk, Lupini and Panagiotopoulus developed the foundations of a field known as `definable algebraic topology,' in which classical cohomological invariants are enriched by viewing them as groups with a Polish…
Based on the Carath\'eodory -Pesin structure theory[11], we introduce three notions of topological pressure of a proper map and provide some properties of these notions. For the proper map of a locally compact separable metric space, we…
This is an article on the interaction between topology and physics which will appear in 1998 in a book called: A History of Topology, edited by Ioan James and published by Elsevier-North Holland.
In the first part of the work (Sections 2-6) a special attention is given to relative separation axioms and relative connectedness, in particular, many relative versions of p-T_0, p-T_1, p-T_2, (i,j)- and p-regularities, (i,j)- and…
This habilitation thesis summarizes the research that I have carried out from 2005 to 2019. It is organized in four chapters. The first three deal with random planar maps. Chapter 1 is about their metric properties: from a general…
Covering problems belong to the foundation of graph theory. There are several types of covering problems in graph theory such as covering the vertex set by stars (domination problem), covering the vertex set by cliques (clique covering…
In recent years considerable advances have been made in quantitative homogenization of partial differential equations in the periodic and non-periodic settings. This monograph surveys the theory of quantitative homogenization for…
This issue contains, in addition to the usual contents, a special festive announcement: A book. This book by Banakh and Zdomsky seems to be the first in a planned series by these authors. We believe that the book will become a cornerstone…
A classic problem in analysis is to solve nonlinear equations of the form \begin{equation*} F(x)=0, \end{equation*} where $F:D^n\to \mathbb{R}^m$ is a continuous map of the closed unit disk $D^n\subset\mathbb{R}^n$ in $\mathbb{R}^m$. A…
We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. Starting from ZFC, the exposition in this first part includes relation and order theory as well as a construction of…
We consider the Lorenz equations, a system of three dimensional ordinary differential equations modeling atmospheric convection. These equations are chaotic and hard to study even numerically, and so a simpler "geometric model" has been…
Recent developments of affine algebraic geometry, especially the theory of open algebraic surfaces, provide means to systematically explore geometric and topological properties of polynomials in two variables. Nevertheless, there is one…
This book concentrates on functional analysis. The text is written so that it can be followed on the basis of high school mathematics. The book introduces the set theoretical foundations of mathematics, the basic theories of linear algebra…
This paper revisits two classical distributed problems in anonymous networks, namely spanning tree construction and topology recognition, from the point of view of graph covering theory. For both problems, we characterize necessary and…
This is a part survey part research paper studying the local topology of complex analytic spaces. We review and strengthen the results of Kapovich--Koll\'ar "Fundamental groups of links of isolated singularities" (1109.4047) and incorporate…
This article is one of three highly influential articles on the topology of manifolds written by Robert D. Edwards in the 1970's but never published. Organizers of the Workshops in Geometric Topology…
Parking problems derive from works in combinatorics by Konheim and Weiss in the 1960s. In a memorable contribution, Lackner and Panholzer (2016) studied parking on a random tree and established a phase transition for this process when \(m…