This survey is intended primarily for two readerships: general topologists who know a little model theory, and model theorists who know a little general topology. Both camps can boast a healthy constituency, and most of this paper should be readily accessible to anyone in either. The ultraproduct construction has a long and distinguished history. While its beginnings go back to the 1930s with K...

A generalized ordered space (a GO-space) is a triple (X, τ,<) where (X,<) is a linearly ordered set and τ is a Hausdorff topology on X that has a base of order-convex sets. If τ is the usual open interval topology of the order <, then we say that (X, τ,<) is a linearly ordered topological space (LOTS). Besides the usual real line, probably the most familiar examples of GO-spaces are the Sorgenf...

Predicting the functional consequences of biodiversity loss in realistic, multitrophic communities remains a challenge. No existing biodiversity-ecosystem function study to date has simultaneously incorporated information on species traits, network topology, and extinction across multiple trophic levels, while all three factors are independently understood as critical drivers of post-extinction...

Crystals of a cobalt(II) 3-amino-1,2,4-triazolate; Co(2)Cl(C(2)N(4)H(3))(3), 1 can be formed from a hydrothermal synthesis. X-Ray crystallography shows an extended 3-dimensional network structure within a hexagonal space group with a=9.9655(7) and c=7.7523(7) A. The data reveal an orientational disorder to the ligand. Structural considerations suggest that the ligand orientation is strongly cor...

We consider the twin paradox of special relativity in a universe with a compact spatial dimension. Such topology allows two twin observers to remain inertial yet meet periodically. The paradox is resolved by considering the relationship of each twin to a preferred inertial reference frame which exists in such a universe because global Lorentz invariance is broken. The twins can perform “global”...

Being the crossroads between Algebra, Topology, Logic, Set Theory and the Theory of Order; the class of Boolean algebras over partially ordered sets were look at as one of the sources, providing over time, new insights in Boolean algebras. Some constructions and their interconnections will be discussed, motivating along the way a list of open problems. Mathematics Subject Classification (MSC 20...

We study a generic problem of proving semantic completeness of a logical system with respect to a class of “standard models”, provided a weaker completeness result with respect to a larger class of “general models” has been obtained. We propose a natural topological approach to this problem based on the notion of logical topology and the related concept of logical approximation. We then obtain ...

The space of one-sided infinite words plays a crucial rôle in several parts of Theoretical Computer Science. Usually, it is convenient to regard this space as a metric space, the CANTOR space. It turned out that for several purposes topologies other than the one of the CANTOR space are useful, e.g. for studying fragments of first-order logic over infinite words or for a topological characterisa...

Network studies of human brain structural connectivity have identified a specific set of brain regions that are both highly connected and highly central. Recent analyses have shown that these putative hub regions are mutually and densely interconnected, forming a "rich club" within the human brain. Here we show that the set of pathways linking rich club regions forms a central high-cost, high-c...