Related papers: Topology on diffeological vector spaces

We consider the intersection map on the family of non-empty $\omega$-Scott-open sets of the lattice of opens of a topological space. We prove that in a certain class of topological spaces the intersection map forms a continuous retraction…

In this thesis, we introduce the subject of D-spaces and some of its most important open problems which are related to well known covering properties. We then introduce a new approach for studying D-spaces and covering properties in…

We establish a structure theorem on the arc space of a $k$-scheme of finite type. More precisely, we show that the arc space is locally for the pro-smooth toplogy a product of an infinite dimensional affine space and of a non-noetherian…

A tensor space is a vector space equipped with a finite collection of multi-linear forms. In recent years, a rich theory of infinite dimensional tensor spaces has emerged. In this note, we show that a large class of permutation groups can…

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…

Let R be a commutative, noetherian, local ring. Topological Q-vector spaces modelled on full subcategories of the derived category of R are constructed in order to study intersection multiplicities.

We discuss algebraic vector bundles on smooth k-schemes X contractible from the standpoint of A^1-homotopy theory; when k = C, the smooth manifolds X(C) are contractible as topological spaces. The integral algebraic K-theory and integral…

The Torelli group of a manifold is the group of all diffeomorphisms which act as the identity on the homology of the manifold. In this paper, we calculate the invariant part (invariant under the action of the automorphisms of the homology)…

The concept of typed topological space is introduced, for which open sets in a topology on a finite set will be assigned types (from lattice). The neighborhood system of a point, the closure and the connectedness can be defined according to…

It is proved that any countable topological vector space over a finite field $\mathbb F_p$ or, equivalently, any countable Abelian topological group of prime exponent has a closed discrete basis.

We classify the topological terms (in a sense to be made precise) that may appear in a non-linear sigma model based on maps from an arbitrary worldvolume manifold to a homogeneous space $G/H$ (where $G$ is an arbitrary Lie group and $H…

It is shown that the diffeomorphism type of the complement to a real space line arrangement in any dimensional affine ambient space is determined only by the number of lines and the data on multiple points.

Convergence is a fundamental topic in analysis that is most commonly modelled using topology. However, there are many natural convergences that are not given by any topology; e.g., convergence almost everywhere of a sequence of measurable…

In this note, we investigate some topological properties of probabilistic modular spaces.

We present several aspects of the "topology of meromorphic functions", which we conceive as a general theory which includes the topology of holomorphic functions, the topology of pencils on quasi-projective spaces and the topology of…

In this paper, we define locally convex vector spaces of weighted vector fields and use them as model spaces for Lie groups of weighted diffeomorphisms on Riemannian manifolds. We prove an easy condition on the weights that ensures that…

We construct a model category structure on the category of diffeological spaces which is Quillen equivalent to the model structure on the category of topological spaces based on the notions of Serre fibrations and weak homotopy…

A mixed lattice vector space is a partially ordered vector space with two partial orderings, generalizing the notion of a Riesz space. Whereas the algebraic theory of mixed lattice structures dates back to the 1970s, the topological theory…

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…

Following the concept of topological theory of S.~E.~Rodabaugh, this paper introduces a new approach to (lattice-valued) bornology, which is based in bornological theories, and which is called variety-based bornology. In particular,…