相关论文: Problems from Topology Proceedings

This article recounts the interaction of topology and singularity theory (mainly singularities of complex algebraic varieties) which started in the early part of this century and bloomed in the 1960's with the work of Hirzebruch, Brieskorn,…

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…

The class of LOTS (linearly ordered topological spaces, i.e. spaces equipped with a topology generated by a linear order) contains many important spaces, like the set of real numbers, the set of rational numbers and the ordinals. Such…

This is a renovated list of open problems, to appear in: "Affine Algebraic Geometry" conference Proceedings volume in Contemporary Mathematics series of the Amer. Math. Soc. Ed. by Jaime Gutierrez, Vladimir Shpilrain, and Jie-Tai Yu.

The paper consists of lecture notes for a mini-course given by the authors at the G\"okova Geometry \& Topology conference in May 2014. We start the exposition with tropical curves in the plane and their applications to problems in…

This contains Part I of the book: Congruence lattices of finite lattices, which covers about 80 years of research and more than 250 papers.

Here we present in a single essay a combination and completion of the several aspects of the problem of randomness of individual objects which of necessity occur scattered in our texbook "An Introduction to Kolmogorov Complexity and Its…

Topos theory occupies a singular place in contemporary mathematics: born from Grothendieck's algebraic geometry, it has emerged as a unifying language for geometry, topology, algebra, and logic. This book offers a progressive introduction…

Toric topology emerged in the end of the 1990s on the borders of equivariant topology, algebraic and symplectic geometry, combinatorics and commutative algebra. It has quickly grown up into a very active area with many interdisciplinary…

The textbook contains the problems in mechanics and special relativity for physics departments of universities. Many original problems were proposed by active scientists from the institutes of the Siberian Branch of Russian Academy of…

Problem 540 of J. D. Lawson and M. Mislove in Open Problems in Topology asks whether the process of taking duals terminate after finitely many steps with topologies that are duals of each other. The problem for $T_1$ spaces was already…

This is a collection of teaching materials used in several Russian universities, schools, and mathematical circles. Most problems are chosen in such a way that in the course of the solution and discussion a reader learns important…

This version is the last version of our book project on Hamilton-Jacobi Equations and Control Problems with discontinuities. Compared to the third version (online in december 2022), we have improved Part V (Stratified solutions for…

This paper presents fifteen problems about mapping class groups. It is an expanded and updated version of the author's preprint "Ten problems on the mapping class groups". The paper will appear in the book "Problems on Mapping Class Groups…

This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century.…

Originally published as a Supplemental Appendix to Adjoint Equations in Stability Analysis, Annu. Rev. Fluid Mech. 46:493-517 (2014)

The manual contains (in Russian) solutions of 230 problems that were used by the author for a number of years at the tutorial seminars in the first year undergraduate course in Mechanics and special relativity at Novosibirsk State…

In this note research and publications by Zdzis{\l}aw Pawlak and his collaborators from 1970s and 1981 are recalled. Focus is placed on the sources of inspiration which one can identify on the basis of those publications. Finally,…

We answer several questions of I.Protasov and E.Zelenyuk concerning topologies on groups determined by T-sequences. A special attention is paid to studying the operation of supremum of two group topologies.

A quick overview of category theory and topos theory including slice categories, monics, epics, isos, diagrams, cones, cocones, limits, colimits, products and coproducts, pushouts and pullbacks, equalizers and coequalizers, initial and…