Related papers: Finite-dimensional diffeological vector spaces bei…
This paper deals with some basic constructions of linear and multilinear algebra on finite-dimensional diffeological vector spaces. We consider the diffeological dual formally checking that the assignment to each space of its dual defines a…
We consider here the category of diffeological vector pseudo-bundles, and study a possible extension of classical differential geometric tools on finite dimensional vector bundles, namely, the group of automorphisms, the frame bundle, the…
In this note, we find a sharp bound for the minimal number (or in general, indexing set) of subspaces of a fixed (finite) codimension needed to cover any vector space V over any field. If V is a finite set, this is related to the problem of…
It is known that the only finite-dimensional diffeological vector space that admits a diffeologically smooth scalar product is the standard space of appropriate dimension. In this note we consider a way to circumnavigate this issue, by…
Near-vector spaces extend linear algebra tools to non-linear algebraic structures, enabling the study of non-linear problems. However, explicit constructions remain rare. This paper introduces a broad computable family of near-vector…
We study the relationship between many natural conditions that one can put on a diffeological vector space: being fine or projective, having enough smooth (or smooth linear) functionals to separate points, having a diffeology determined by…
It is expected that the $D$-topology makes every diffeological vector space into a topological vector space. We show that it is the case for a large class of diffeological vector spaces via $k_\omega$-space theory, but not so in general.…
The aim of this work is to offer a family of invariants that allows us to classify finite potent endomorphisms on arbitrary vector spaces, generalizing the classification of endomorphisms on finite-dimensional vector spaces. As a particular…
We investigate infinite versions of vector and affine space partition results, and thus obtain examples and a counterexample for a partition problem for relational structures. In particular we provide two (related) examples of an age…
We provide a characterization of the finite dimensionality of vector spaces in terms of the right-sided invertibility of linear operators on them.
If a compact closed category has finite products or finite coproducts then it in fact has finite biproducts, and so is semi-additive.
A ringed finite space is a ringed space whose underlying topological space is finite. The category of ringed finite spaces contains, fully faithfully, the category of finite topological spaces and the category of affine schemes. Any ringed…
We consider the dimensions of finite type of representations of a partially ordered set, i.e. such that there is only finitely many isomorphism classes of representations of this dimension. We give a criterion for a dimension to be of…
For a field $\ef$, the discrete topological vector spaces over $\ \ef$ are essentially of the form $\ef^{\alpha}$ where $\alpha$ is an ordinal. With additional appropriate properties, they are isomorphic to $\ef^{(\beta)}$ where $\beta$ is…
We characterize the families of bialgebras or Hopf algebras over fields for which the product in the corresponding category is finite-dimensional, answering a question of M. Lorenz: if the ground field is infinite then bialgebra or Hopf…
In this paper we consider the complex vector spaces of holomorphic cross-sections of homogeneous holomorphic vector bundles over elliptic adjoint orbits, and provide a sufficient condition for the vector spaces to be finite dimensional in…
We consider the class of profinite diffeological spaces, that is, diffeological spaces which diffeologies are deduced by pull-back of diffeologies on finite-dimensional manifolds through a system of projection mappings. This class includes…
In this paper we extend our findings in [3] and answer further questions regarding continuity and discontinuity of seminorms on infinite-dimensional vector spaces.
A vector space is commonly defined as a set that satisfies several conditions related to addition and scalar multiplication. However, for beginners, it may be hard to immediately grasp the essence of these conditions. There are probably a…
A ringed finite space is a ringed space whose underlying topological space is finite. The category of ringed finite spaces contains, fully faithfully, the category of finite topological spaces and the category of affine schemes. Any ringed…