Sequential convergence in topological spaces

In this survey, my aim has been to discuss the use of sequences and countable sets in general topology. In this way I have been led to consider five different classes of topological spaces: first countable spaces, sequential spaces, Frechet spaces, spaces of countable tightness and perfect spaces. We are going to look at how these classes are related, and how well the various properties behave under certain operations, such as taking subspaces, products, and images under proper mappings. Where they are not well behaved we take the opportunity to consider some relevant examples, which are often of special interest. For instance, we examine an example of a Frechet space with unique sequential limits that is not Hausdorff. I asked the question of whether there exists in ZFC an example of a perfectly normal space that does not have countable tightness: such an example was supplied and appears below. In our discussion we shall report two independence theorems, one of which forms the solution to the Moore-Mrowka problem. The results that we prove below include characterisation theorems of sequential spaces and Frechet spaces in terms of appropriate classes of continuous mappings, and the theorem that every perfectly regular countably compact space has countable tightness.Comment: 29 pages. This version incorporates the correction of Proposition 3.2 to include an additional assumption (Hausdorff), whose necessity has been pointed out by Alexander Gouberma

Modeling Flocks and Prices: Jumping Particles with an Attractive Interaction

We introduce and investigate a new model of a finite number of particles jumping forward on the real line. The jump lengths are independent of everything, but the jump rate of each particle depends on the relative position of the particle compared to the center of mass of the system. The rates are higher for those left behind, and lower for those ahead of the center of mass, providing an attractive interaction keeping the particles together. We prove that in the fluid limit, as the number of particles goes to infinity, the evolution of the system is described by a mean field equation that exhibits traveling wave solutions. A connection to extreme value statistics is also provided.Comment: 35 pages, 9 figures. A shortened version appears as arXiv:1108.243

Solving Functional Constraints by Variable Substitution

Functional constraints and bi-functional constraints are an important constraint class in Constraint Programming (CP) systems, in particular for Constraint Logic Programming (CLP) systems. CP systems with finite domain constraints usually employ CSP-based solvers which use local consistency, for example, arc consistency. We introduce a new approach which is based instead on variable substitution. We obtain efficient algorithms for reducing systems involving functional and bi-functional constraints together with other non-functional constraints. It also solves globally any CSP where there exists a variable such that any other variable is reachable from it through a sequence of functional constraints. Our experiments on random problems show that variable elimination can significantly improve the efficiency of solving problems with functional constraints

In-Work Benefits and Unemployment

In-work benefits are becoming an increasingly relevant labour market policy, gradually expanding in scope and geographical coverage. This paper investigates the equilibrium impact of in-work benefits and contrasts it with the traditional partial equilibrium analysis. We find under which conditions accounting for equilibrium wage adjustments amplifies the impact of in-work benefits on search intensity, participation, employment, and unemployment, compared to a framework in which wages are fixed. We also account for the financing of these benefits and determine the level of benefits necessary to achieve efficiency in a labour market characterized by search externalities.search, in-work benefits, labour force participation, wage adjustment

Classification of tight contact structures on small Seifert fibered L-spaces

The Ozsvath-Szabo contact invariant is a complete classification invariant for tight contact structures on small Seifert fibered 3-manifolds which are L-spaces.Comment: 30 pages, 3 figure