Related papers: Lineability criteria, with applications

A variety $X$ is covered by lines if there exist a finite number of lines contained in $X$ passing through each general point. I prove two theorems. Theorem 1:Let $X^n\subset P^M$ be a variety covered by lines. Then there are at most $n!$…

In this paper, we study the property of hereditary completeness of vector systems $\{x_k\}_{k=1}^\infty$ in a Hilbert space. A criterion of hereditary completeness is obtained in terms of projectors on closed linear spans of systems of the…

If $X$ is a (topological) space, the $n$th finite subset space of $X$, denoted by $X(n)$, consists of $n$-point subsets of $X$ (i.e., nonempty subsets of cardinality at most $n$) with the quotient topology induced by the unordering map…

This manuscript studies statistical properties of linear classifiers obtained through minimization of an unregularized convex risk over a finite sample. Although the results are explicitly finite-dimensional, inputs may be passed through…

Patterns on numerical semigroups are multivariate linear polynomials, and they are said to be admissible if there exists a numerical semigroup such that evaluated at any nonincreasing sequence of elements of the semigroup gives integers…

The concept of robustness of regulatory networks has been closely related to the nature of the interactions among genes, and the capability of pattern maintenance or reproducibility. Defining this robustness property is a challenging task,…

It is shown that an ordered vector space $X$ is Archimedean if and only if $\inf\limits_{\tau\in\{\tau\}, y\in L}(x_\tau -y) \ = 0$ for any bounded decreasing net $x_\tau\downarrow$ in $X$, where $L$ is the collection of all lower bounds of…

An algebraic criterion that is sufficient to establish the existence of certain a priori estimates for the solution of first-order homogeneous linear characteristic problems is derived. Estimates of such kind ensure the stability of the…

In this paper we introduce a new technique to prove the existence of closed subspaces of maximal dimension inside sets of topological vector sequence spaces. The results we prove cover some sequence spaces not studied before in the context…

A convex subset X of a linear topological space is called compactly convex if there is a continuous compact-valued map $\Phi:X\to exp(X)$ such that $[x,y]\subset\Phi(x)\cup \Phi(y)$ for all $x,y\in X$. We prove that each convex subset of…

This paper is inspired by the paper of Leonetti, Russo and Somaglia [\textit{Dense lineability and spaceability in certain subsets of $\ell_\infty$.} Bull. London Math. Soc., 55: 2283--2303 (2023)] and the lineability problems raised…

Functions with uniform level sets can represent orders, preference relations or other binary relations and thus turn out to be a tool for scalarization that can be used, e.g., in multicriteria optimization, decision theory, mathematical…

The density topology $\cal T$ is a topology on the real line, finer than the usual topology, having as its open sets the measurable subsets of ${\mathbb R}$, which are of density 1 at each of their points. The aim of this paper is to…

For a collection of subcategories satisfying a fixed set of conditions, for example thick subcategories of a triangulated category, we define a topological space called classifying space of subcategories. We show that this space classifies…

A point $p\in\mathbb{P}^N$ of a projective space is $h$-identifiable, with respect to a variety $X\subset\mathbb{P}^N$, if it can be written as linear combination of $h$ elements of $X$ in a unique way. Identifiability is implied by…

In the paper, notions of relative separability for hypergraphs of models of a theory are defined. Properties of these notions and applications to ordered theories are studied: characterizations of relative separability both in a general…

A large literature specifies conditions under which the information complexity for a sequence of numerical problems defined for dimensions $1, 2, \ldots$ grows at a moderate rate, i.e., the sequence of problems is tractable. Here, we focus…

The (chordal) Loewner differential equation encodes certain curves in the half-plane (aka traces) by continuous real-valued driving functions. Not all curves are traces; the latter can be defined via a geometric condition called the local…

In this paper we suggest new effective criteria for the density property. This enables us to give a trivial proof of the original Anders\'en-Lempert result and to establish (almost free of charge) the algebraic density property for all…

Topological models of empirical and formal inquiry are increasingly prevalent. They have emerged in such diverse fields as domain theory [1, 16], formal learning theory [18], epistemology and philosophy of science [10, 15, 8, 9, 2],…