Related papers: Finite-dimensional diffeological vector spaces bei…

We prove various results in infinite-dimensional differential calculus which relate differentiability properties of functions and associated operator-valued functions (e.g., differentials). The results are applied in two areas: 1. in the…

Let $V$ be a vector space with countable dimension over a field, and let $u$ be an endomorphism of it which is locally finite, i.e. $(u^k(x))_{k \geq 0}$ is linearly dependent for all $x$ in $V$. We give several necessary and sufficient…

We revisit tensor algebras of subproduct systems with Hilbert space fibers, resolving some open questions in the case of infinite dimensional fibers. We characterize when a tensor algebra can be identified as the algebra of uniformly…

Multivector fields and differential forms at the continuum level have respectively two commutative associative products, a third composition product between them and various operators like $\partial$, $d$ and $*$ which are used to describe…

The metric dimension of non-component graph, associated to a finite vector space, is determined. It is proved that the exchange property holds for resolving sets of the graph, except a special case. Some results are also related to an…

An almost periodic function in finite-dimensional space extends to a holomorphic bounded function in a tube domain with a cone in the base if and only if the spectrum belongs to the conjugate cone. Also, an almost periodic function in…

We study completions of Archimedean vector lattices relative to any nonempty set of positively-homogeneous functions on finite-dimensional real vector spaces. Examples of such completions include square mean closed and geometric closed…

We provide base change theorems, projection formulae and Verdier duality for both cohomology and homology in the context of finite topological spaces

We show that for any pair of non-trivial finite groups, their coproduct in the category of finite groups is not representable.

We prove that if a subset of the d-dimensional vector space over a finite field is large enough, then it contains many k-tuples of mutually orthogonal vectors.

We prove that every endomorphism of an infinite-dimensional vector space splits as the sum of four idempotents and as the sum of four square-zero endomorphisms, a result that is optimal in general.

We show that the tensor product of modules of tensor fields is a noetherian module as a module over any graded Lie subalgebra of finite codimension in the Lie algebra of polynomial vector fields on $\mathbb{R}^n$. As a corollary, we prove…

We study the structure of two-sided vector spaces over a perfect field $K$. In particular, we give a complete characterization of isomorphism classes of simple two-sided vector spaces which are left finite-dimensional. Using this…

We exhibit a set of generating relations for the modular invariant ring of a vector and a covector for the two-dimensional general linear group over a finite field.

It is well known that not every convex multifunction admits an affine selection. One could ask whether there exists at least local affine selection. The answer is positive in the finite-dimensional case. The main part of this note consists…

In this paper we discuss some properties of completely irrational subspaces. We prove that there exist completely irrational subspaces that are badly approximable and, moreover, sets of such subspaces are winning in different senses. We get…

A subspace arrangement in a vector space is a finite collection of vector subspaces. Similarly, a configuration of linear spaces in a projective space is a finite collection of linear subspaces. In this paper we study the degree 2 part of…

We prove extension-dimensional versions of finite dimensional selection and approximation theorems. As applications, we obtain several results on extension dimension.

In this paper we develop a duality theory for all finite-dimensional near-vector spaces and introduce a notion of inner product tailored to the broad and natural class of strongly regular near-vector spaces. This generalized construction…

We discuss an elementary, yet unsolved, problem of Niederreiter concerning the enumeration of a class of subspaces of finite dimensional vector spaces over finite fields. A short and self-contained account of some recent progress on this…