Related papers: Duality of Discrete Topological Vector Spaces
Strata of exact differentials are moduli spaces for differentials on Riemann surfaces with vanishing absolute periods. Our main result is that classes of closures of strata of exact differentials inside the moduli space of multi-scale…
We show that if two tensor algebras of topological graphs are algebraically isomorphic, then the graphs are locally conjugate. Conversely, if the base space is at most one dimensional and the edge space is compact, then locally conjugate…
Cobordism categories have played an important role in classical geometry and more recently in mathematical treatments of quantum field theory. Here we will compute localisations of two-dimensional discrete cobordism categories. This allows…
In this manuscript, we will study both $\tilde{o}$-convergence in (partially) ordered vector spaces and a kind of convergence in a vector space $V$. A vector space $V$ is called semi-order vector space (in short semi-order space), if there…
We study Vietoris hyperspaces of closed and closed final sets of Priestley spaces. We are particularly interested in Skula topologies. A topological space is \emph{Skula} if its topology is generated by differences of open sets of another…
On the affine space containing the space $\mathcal{S}$ of quantum states of finite-dimensional systems there are contravariant tensor fields by means of which it is possible to define Hamiltonian and gradient vector fields encoding relevant…
A modular tensor category provides the appropriate data for the construction of a three-dimensional topological field theory. We describe the following analogue for two-dimensional conformal field theories: a 2-category whose objects are…
We study strong linearisations and the uniqueness of preduals of locally convex Hausdorff spaces of scalar-valued functions. Strong linearisations are special preduals. A locally convex Hausdorff space $\mathcal{F}(\Omega)$ of scalar-valued…
We show some examples of topological zeta functions associated to an isolated plane curve singular point and an allowed, in the sense of N\'emethi and Veys, differential form that have several poles of order two. This is in contrast to the…
In this paper we give description of free and cofree objects in the category of operator sequence spaces. First we show that this category possess the same duality theory as category of normed spaces, then with the aid of these results we…
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.
The classification of algebraic vector bundles of rank 2 over smooth affine fourfolds is a notoriously difficult problem. Isomorphism classes of such vector bundles are not uniquely determined by their Chern classes, in contrast to the…
Topology may be interpreted as the study of verifiability, where opens correspond to semi-decidable properties. In this paper we make a distinction between verifiable properties themselves and processes which carry out the verification…
Transports preserving the angle between two contravariant vector fields but changing their lengths proportional to their own lengths are introduced as `conformal' transports and investigated over spaces with one affine connection and…
Several div-conforming and divdiv-conforming finite elements for symmetric tensors on simplexes in arbitrary dimension are constructed in this work. The shape function space is first split as the trace space and the bubble space. The later…
The present article studies decompositions of vector bundles on the moduli stack of elliptic curves that are pushforwards of vector bundles on moduli of elliptic curves with level structure. These imply decomposition results for rings of…
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…
We survey results on the topological complexity of classical configuration spaces of distinct ordered points in orientable surfaces and related spaces, including certain orbit configuration spaces and Eilenberg-Mac Lane spaces associated to…
Some zeta functions which are naturally attached to the locally homogeneous vector bundles over compact locally symmetric spaces of rank one are investigated. We prove that such functions can be expressed in terms of entire functions whose…
Subspace varieties are algebraic varieties whose elements are tensors with bounded multilinear rank. In this paper, we compute their degrees by computing their volumes.