The main purpose of this paper is to investigate constructively the relationship between proximal convergence, uniform sequential convergence and uniform convergence for sequences of mappings between apartness spaces. It is also shown that if the second space satisfies the Efremovic axiom, then proximal convergence preserves strong continuity. Mathematics Subject Classification: 54E05, 03F60

An Open Coloring Axiom type principle is formulated for uncountable cardinals and is shown to be a consequence of the Proper Forcing Axiom. Several applications are found. We also study dense C∗-embedded subspaces of ω∗, showing that there can be such sets of cardinality c and that it is consistent that ω∗ \ {p} is C∗-embedded for some but not all p ∈ ω∗.

We introduce ‘subgroup additivity’ as our main axiom and investigate its implications for the queueing problem. The axiom of subgroup additivity requires that a rule assigns the same expected ‘relative’ utility to each agent whether an agent’s expected relative utility is calculated from the problem involving all agents or from its sub-problems with a smaller number of agents. As a result, we p...

Quality control is an essential task within ontology development projects especially when the knowledge formalization is partially automatized. In this paper, we propose a reasoning-based, interactive approach to support the revision of formalized knowledge. We state consistency criteria for revision states and introduce the notion of revision closure, based on which the revision of ontologies ...

For Axiom A diffeomorphisms and equilibrium states, we prove a Large deviations result for the sequence of successive return times into a fixed Borel set, under some assumption on the boundary. Our result relies on and extends the work by Chazottes and Leplaideur who considered cylinder sets of a Markov partition.

We introduce a new reflection principle which we call “Fodor-type Reflection Principle” (FRP). This principle follows from but is strictly weaker than Fleissner’s Axiom R. For instance, FRP does not impose any restriction on the size of the continuum, while Axiom R implies that the continuum has size ≤ א2. We show that FRP implies that every locally separable countably tight topological space X...

Verjovsky stated the conjecture in [35] for all dimensions with an additional assumption that the fundamental group of the manifold is solvable. This was proved by Plante [24, 25] and Armendariz [4], who showed that the conjecture is true if and only if the fundamental group of the manifold is solvable. In the above form, the conjecture first appeared in Ghys [13]. However, Ghys has pointed out...

This paper is an introduction to forcing axioms and large cardinals. Specifically, we shall discuss the large cardinal strength of forcing axioms in the presence of regularity properties for projective sets of reals. The new result shown in this paper says that ZFC + the bounded proper forcing axiom (BPFA) + “every projective set of reals is Lebesgue measurable” is equiconsistent with ZFC + “th...

An important contemporary debate (going back to (Gödel, 1964)) in the philosophy of mathematics is whether or not mathematics needs new axioms. This paper is an attempt to show how one might go about answering this question. I argue that the role of axioms is to allow mathematicians to stay away from philosophical debates, and thus focus on their primary goal of proving interesting theorems. I ...

Abstract Graphical (Linear) Algebra is a family of diagrammatic languages allowing to reason about different kinds subsets vector spaces compositionally. It has been used model various application domains, from signal-flow graphs Petri nets and electrical circuits. In this paper, we introduce the its most expressive member date: Piecewise-Linear Algebra, new language specify piecewise-linear sp...