Related papers: Some new directions in infinite-combinatorial topo…
We review some selected recent results concerning selection principles in topology and their relations with several topological constructions.
We survey some of the major open problems involving selection principles, diagonalizations, and covering properties in topology and infinite combinatorics. Background details, definitions and motivations are also provided.
Motivated by a recent result of Sakai, we define a new selection operator for covers of topological spaces, inducing new selection hypotheses. We initiate a systematic study of the new hypotheses. Some intriguing problems remain open.
In the year 2014, the field of selection principles found its way into several additional, fascinating mathematical realms. The field enters the consensus as a mainstream part of set theory and topology, and as a promising direction for…
We present an analysis of the topologies of a class of networks which are optimal in terms of the requirements of having as short a route as possible between any two nodes while yet keeping the congestion in the network as low as possible.…
We continue to investigate applications of $k$-covers in function spaces with the compact-open topology.
We use the recently introduced \'etale open topology to prove several facts about large fields. We show that these facts lift to a very general topological setting.
An S-approximation space is a novel approach to study systems with uncertainty that are not expressible in terms of inclusion relations. In this work, we further examined these spaces, mostly from a topological point of view by a…
We begin the study of the consequences of the existence of certain infinite matrices. Our present application is to compactness of products of topological spaces.
The topological classification of all known non-magnetic crystalline compounds is now complete, revealing thousands of new candidate topological materials waiting to be explored in the lab.
An old branch of mathematics, Topology, has opened the road to the discovery of new phases of matter. A hidden topology in the energy spectrum is the key for novel conducting/insulating properties of topological matter.
We give a characterization of completely regular topological spaces. Applying some recent results for supinf problems in completely regular topological spaces we establish a variational principle for saddle points. Well-posedness of saddle…
Ideas from quantum field theory and topology have proved remarkably fertile in suggesting new phenomena in the quantum physics of condensed matter. Here I'll supply some broad, unifying context, both conceptual and historical, for the…
More than two decades ago, combinatorial topology was shown to be useful for analyzing distributed fault-tolerant algorithms in shared memory systems and in message passing systems. In this work, we show that combinatorial topology can also…
This is the first issue of a semi-formal bulletin dealing with Selection Principles in Mathematics (SPM) -- this field deals with all sorts of studies of diagonalization arguments, especially in topology (covering properties, sequences of…
In this paper we develop new extremal principles in variational analysis that deal with finite and infinite systems of convex and nonconvex sets. The results obtained, unified under the name of tangential extremal principles, combine primal…
This survey presents some historical background and recent developments in the area of selections for set-valued mappings along with several open questions. It was written with the hope that the presented material may pique an interest in…
Topological photonics is emerging as a new paradigm for the development of both classical and quantum photonic architectures. What makes topological photonics remarkably intriguing is the built-in protection as well as intrinsic…
This is a survey of recent developments in combinatorics. The goal is to give a big picture of its many interactions with other areas of mathematics, such as: group theory, representation theory, commutative algebra, geometry (including…
We present a new variation of the classical selection principles $\mathsf{S}_\mathrm{k}(\mathcal A, \mathcal B)$ ($k\in\mathbb N$) and $\mathsf{S}_\mathrm{fin}(\mathcal A, \mathcal B)$ that formally lies between these two properties. As in…