Related papers: Transfinite Sequences of Continuous and Baire Clas…
A compact space $X$ is called $\pi$-monolithic if for any surjective continuous mapping $f:X\rightarrow K$ where $K$ is a metrizable compact space there exists a metrizable compact space $T\subseteq X$ such that $f(T)=K$. A topological…
By using the space of fuzzy numbers, in e.g. [5] have been considered several complete metric spaces (called here {\bf FN}-type spaces) endowed with addition and scalar multiplication, such that the metrics have nice properties but the…
We characterize the existence of a nonnegative, sublinear and continuous order-preserving function for a not necessarily complete preorder on a real convex cone in an arbitrary topological real vector space. As a corollary of the main…
In the previous decades, the theory of first passage percolation became a highly important area of probability theory. In this work, we will observe what can be said about the corresponding structure if we forget about the probability…
In this paper we look for the existence of large linear and algebraic structures of sequences of measurable functions with different modes of convergence. Concretely, the algebraic size of the family of sequences that are convergent in…
A person is given a numbered sequence of positions on a sheet of paper. The person is asked, "Which will be the next (or the next after that) position?" Everyone has an opinion as to how he or she would proceed. There are regular sequences…
The paper deals with variational approaches to the segmentation of time series into smooth pieces, but allowing for sharp breaks. In discrete time, the corresponding functionals are of Blake-Zisserman type. Their natural counterpart in…
We show that for arbitrary linearly ordered set $X$ any bounded family of (not necessarily, continuous) real valued functions on $X$ with bounded total variation does not contain independent sequences. We obtain generalized Helly's…
Partial orders are used extensively for modeling and analyzing concurrent computations. In this paper, we define two properties of partially ordered sets: width-extensibility and interleaving-consistency, and show that a partial order can…
We introduce the notion of $B_1$-retract and investigate the connection between $B_1$- and $H_1$-retracts.
Every definably complete expansion of an ordered field satisfies an analogue of the Baire Category Theorem.
We introduce vectorial and topological continuities for functions defined on vector metric spaces and illustrate spaces of such functions. Also, we describe some fundamental classes of vector valued functions and extension theorems.
We present a first-order theory of sequences with integer elements, Presburger arithmetic, and regular constraints, which can model significant properties of data structures such as arrays and lists. We give a decision procedure for the…
We introduce and study (metrically) quarter-stratifiable spaces and then apply them to generalize Rudin and Kuratowski-Montgomery theorems about the Baire and Borel complexity of separately continuous functions.
Let $\mathcal{L}(X;Y)$ be the space of bounded linear operators from a Banach space $X$ to a Banach space $Y$. Given an operator-valued function $u:\mathbb{R}_{\geq 0}\rightarrow \mathcal{L}(X;Y)$, suppose that every orbit $t\mapsto u(t)x$…
In the study of discrete dynamical systems, we typically start with a function from a space into itself, and ask questions about the properties of sequences of iterates of the function. In this paper we reverse the direction of this study.…
We prove an extension theorem (with non-tangential limits) for vector-valued Baire one functions. Moreover, at every point where the function is continuous (or bounded), the continuity (or boundedness) is preserved. More precisely: Let $H$…
It is studied a connection between the separability and the countable chain condition of spaces with the $L$-property (a topological space $X$ has the $L$-property if for every topological space $Y$, separately continuous function…
This paper is a review containing new original results on the finite order variational sequence and its different representations with emphasis on applications in the theory of variational symmetries and conservation laws in physics.
This paper is motivated by the theory of sequential dynamical systems, developed as a basis for a mathematical theory of computer simulation. It contains a classification of finite dynamical systems on binary strings, which are obtained by…