Related papers: A Note on Hypervector Spaces
The main purpose of this paper is to study the vector groupoids. This is an algebraic structure which combines the concepts of Brandt groupoid and vector space such that these are compatible.
In this paper we introduce the concept of generalized vector groupoid. Several properties of them are established.
We introduce and explore a new concept of evasive subspace with respect to a collection of subspaces sharing a common dimension, most notably partial spreads. We show that this concept generalises known notions of subspace scatteredness and…
Recently, a geometrical characterization of vector spaces served to generalize them into a new class of algebras. Instead of the algebraic properties of the underlying fields, we generalized the recently discovered property of such spaces…
I discuss possible definitions of categories of vector spaces enriched with a notion of formal infinite linear combination in the likes of the formal infinite linear combinations one has in the context of generalized power series, I call…
A new generalization of Grassmannians, called {\nu}-grassmannians, and a canonical super vector bundle over this new space, say {\Gamma}, are introduced. Then, constructing a Gauss supermap of a super vector bundle, the universal property…
In this paper, we prove that the world of near-vector spaces allows us to work with non-linear problems and yet, gives access to most of the tools linear algebra has to offer. We establish some fundamental results for near-vector spaces…
The subject of the paper is the geometry and topology of cosmological spacetimes and vector bundles thereon, which are used to model physical fields propagating in the universe. Global hyperbolicity and factorization properties of the…
In this paper we discuss various philosophical aspects of the hyperstructure concept extending networks and higher categories. By this discussion we hope to pave the way for applications and further developments of the mathematical theory…
We present a concise proof for the supporting hyperplane theorem. We then observe that the proof not only establishes the supporting hyperplane theorem but also extends it to a hyperplane separation theorem for certain non-convex sets. The…
Distributional semantics creates vector-space representations that capture many forms of semantic similarity, but their relation to semantic entailment has been less clear. We propose a vector-space model which provides a formal foundation…
We develop a Hilbert space framework for a number of general multi-scale problems from dynamics. The aim is to identify a spectral theory for a class of systems based on iterations of a non-invertible endomorphism. We are motivated by the…
The notion of {\it free} generalized vertex algebras is introduced. It is equivalent to the notion of {\it generalized principal subspaces} associated with lattices which are not necessarily integral. Combinatorial bases and the characters…
We provide base change theorems, projection formulae and Verdier duality for both cohomology and homology in the context of finite topological spaces
A generalization of metric space is presented which is shown to admit a theory strongly related to that of ordinary metric spaces. To avoid the topological effects related to dropping any of the axioms of metric space, first a new, and…
We develop a vector space semantics for Lambek Calculus with Soft Subexponentials, apply the calculus to construct compositional vector interpretations for parasitic gap noun phrases and discourse units with anaphora and ellipsis, and…
We investigate the most general "phase space" of configurations, consisting of all possible ways of assigning elementary attributes, "energies", to elementary positions, "cells". We discuss how this space possesses structures that can be…
In a series of papers in the 1960's, S. G\"ahler defined and investigated so-called m-metric spaces and their topological properties. An m-metric assigns to any tuple of m+1 elements a real value (more generally an element in a partially…
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…
We provide a complete structure theorem for involutory matrices. This yields a new approach to principal angles between subspaces and provide a series of nice formulae for these angles.