Related papers: Locally Constant Constructive Functions and Connec…
In this paper, we show that a pointwise-symmetric isotonic closure function is uniquely determined by the pairs of sets it separates. We then show that when the closure function of the domain is isotonic and the closure function of the…
Many systems occurring in real-world applications, such as controlling the motions of robots or modeling the spread of diseases, are switched impulsive systems. To ensure that the system state stays in a safe region (e.g., to avoid…
We consider the task of constructing a data structure for associating a static set of keys with values, while allowing arbitrary output values for queries involving keys outside the set. Compared to hash tables, these so-called static…
We call a function constructible if it has a globally subanalytic domain and can be expressed as a sum of products of globally subanalytic functions and logarithms of positively-valued globally subanalytic functions. For any $q > 0$ and…
We study 2-local reflexivity of the set of all surjective isometries between certain function spaces. We do not assume linearity for isometries. We prove that a 2-local isometry in the group of all surjective isometries on the algebra of…
We prove that each closed locally continuum- connected subspace of a finite dimensional topological group is locally compact. This allows us to construct many 1-dimensional metrizable separable spaces that are not homeomorphic to closed…
In this article we introduce new possibilities of bounding the stability constants that play a vital role in the reduced basis method. By bounding stability constants over a neighborhood we make it possible to guarantee stability at more…
We show that any finite set of linear partial differential operators with continuous coefficients is linearly dependent if and only if it is locally linearly dependent. It follows that the reflexive closure of any finite set of such…
We study definably complete locally o-minimal expansions of ordered groups in this paper. A definable continuous function defined on a closed, bounded and definable set behave like a continuous function on a compact set. We demonstrate…
We prove that every nonnegative continuous real-valued function on a given compact metric space is the uniform limit of some increasing sequence of nonnegative simple functions being linear combinations of indicators of open sets; here the…
In contexts in which the principle of dependent choice may not be available, as toposes or Constructive Set Theory, standard locale theoretic results related to complete regularity may fail to hold. To resolve this difficulty, B.…
An important consequence of the Hahn-Banach Theorem says that on any locally convex Hausdorff topological space $X$, there are sufficiently many continuous linear functionals to separate points of $X$. In the paper, we establish a `local'…
A monotone function interval is the set of monotone functions that lie pointwise between two fixed monotone functions. We characterize the set of extreme points of monotone function intervals and apply this to a number of economic settings.…
We consider the class of interval maps with dense set of periodic points CP and its closure Cl(CP) equipped with the metric of uniform convergence. Besides studying basic topological properties and density results in the spaces CP and…
We construct a uniformly expanding map of the interval, preserving Lebesgue measure, such that the corresponding transfer operator admits a spectral gap on the space of Lipschitz functions, but does not act continuously on the space of…
Attractor-repeller decompositions of isolated invariant sets give rise to so-called connecting homomorphisms. These homomorphisms reveal information on the existence and structure of connecting trajectories of the underlying dynamical…
In \cite{Mil}, Milnor posed the {\em Monotonicity Conjecture} that the set of parameters within a family of real multimodal polynomial interval maps, for which the topological entropy is constant, is connected. This conjecture was proved…
Our paper is the first study of what one might call "reverse mathematics of explicit fixpoints". We study two methods of constructing such fixpoints for formulas whose principal connective is the intuitionistic Lewis arrow. Our main…
We show that the closure of the value set of a real linear recurrence sequence is the union of a countable set and a finite collection of intervals. Conversely, any finite collection of closed intervals is the closure of the value set of…
We construct bisymmetric, strictly increasing binary operations on real intervals which are not continuous. This answers a natural question in the theory of bisymmetric and mean-type operations by showing that continuity may fail for…