Related papers: Three open problems on the Wijsman topology
We present some recent results in Fibrewise General Topology with special regard to the theory of Tychonoff compactifications of mappings. Several open problems are also proposed.
Given a finite collection of two-dimensional tile types, the field of study concerned with covering the plane with tiles of these types exclusively has a long history, having enjoyed great prominence in the last six to seven decades. Much…
Manifolds occur naturally as configuration spaces of robotic systems. They provide global descriptions of local coordinate systems that are common tools in expressing positions of robots. The purpose of this survey is threefold. Firstly, we…
We present a brief review of physical problems leading to indefinite Hilbert spaces and non-hermitian Hamiltonians. With the exception of pseudo-Riemannian manifolds in GR, the problem of a consistent physical interpretation of these…
We investigate Whitehead's asphericity question from a new perspective, using results and techniques of the homotopy theory of finite topological spaces. We also introduce a method of reduction to investigate asphericity based on the…
Geodesic nets on Riemannian manifolds form a natural class of stationary objects generalizing geodesics. Yet almost nothing is known about their classification or general properties even when the ambient Riemannian manifold is the Euclidean…
The existence of closed hypersurfaces of prescribed curvature in semi-riemannian manifolds is proved provided there are barriers.
We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. In this second part we introduce the fundamental concepts of topological spaces, convergence, and continuity, as…
We survey two decades of work on the (sequential) topological complexity of configuration spaces of graphs (ordered and unordered), aiming to give an account that is unifying, elementary, and self-contained. We discuss the traditional…
Wheeler emphasized the study of Superspace - the space of 3-geometries on a spatial manifold of fixed topology. This is a configuration space for GR; knowledge of configuration spaces is useful as regards dynamics and QM.In this Article I…
We present a collection of easily stated open problems in the theory of compact constant mean curvature surfaces with boundary. We also survey the current status of answering them.
This book is an account of certain topics in general and algebraic topology. Instead of laying out a synopsis of each chapter, here is a sample of some of what is taken up: 1) Nilpotency and its role in homotopy theory. 2) Bousfield's…
Fifteen years after their discovery, ample fields now stand at the center of research in contemporary Galois theory and attract more and more attention also from other areas of mathematics. This survey gives an introduction to the theory of…
The quest to reveal the physical essence of the infinitely many symmetries and conservation laws that are intrinsic to integrable systems has historically posed a significant challenge at the confluence of physics and mathematics. This…
An algebraization of the notion of topology has been proposed more than seventy years ago in a classical paper by McKinsey and Tarski. However, in McKinsey and Tarski's setting the model theoretical notion of homomorphism does not…
In spite of its long history and classical character which goes back even to d'Alembert and Lagrange, the problems of constraints in mechanics of continua is still mysterious and full of misunderstandings. Let us mention the problem of…
We introduce the concept of a topological J-group and determine for many important examples of topological groups if they are topological J-groups or not. Besides other results, we show that the underlying topological space of a pathwise…
The moduli spaces of compact and connected Riemann surfaces has been a central topic in modern mathematics in recent years. Thus their homological dimensions become important invariants. Motivated by the emergence mathematical counterparts…
Complete and joint mixability has raised considerable interest in recent few years, in both the theory of distributions with given margins, and applications in discrete optimization and quantitative risk management. We list various open…
The aim of this paper is to share with the mathematical community a list of 33 problems that I have found along the years during my research. I believe that it is worth to think about them and, hopefully, it will be possible either to solve…