Related papers: Uniform structures on differential spaces
This paper aims to examine the version of the topological group structure in proximity and especially descriptive proximity spaces, that is, the concepts of proximal group and descriptive proximal group are introduced. In addition, the…
We introduce a notion of a filtered model structure and use this notion to produce various model structures on pro-categories. This framework generalizes several known examples. We give several examples, including a homotopy theory for…
Starting from the observation that distinct notions of copying have arisen in different categorical fields (logic and computation, contrasted with quantum mechanics) this paper addresses the question of when, or whether, they may coincide.…
Definable continuous injective maps defined on definable open sets into the Euclidean spaces of the same dimension are open maps in definably complete locally o-minimal expansions of ordered groups.
A geometric framework for describing quantum particles on a possibly curved background is proposed. Natural constructions on certain distributional bundles (`quantum bundles') over the spacetime manifold yield a quantum ``formalism'' along…
The uniform one-dimensional fragment of first-order logic, U1, is a formalism that extends two-variable logic in a natural way to contexts with relations of all arities. We survey properties of U1 and investigate its relationship to…
We provide a representation of the homomorphisms $U\longrightarrow \mathbb R$, where $U$ is the lattice of all uniformly continuous on the line. The resulting picture is sharp enough to describe the fine topological structure of the space…
A theoretical framework is developed to describe the transformation that distributes probability density functions uniformly over space. In one dimension, the cumulative distribution can be used, but does not generalize to higher…
It is shown that physical fields are formed by physical structures, which in their properties are differential-geometrical structures. These results have been obtained due to using the mathematical apparatus of skew-symmetric differential…
We discuss what is known about the structure of the bounded derived categories of coherent sheaves on Grassmannians of simple algebraic groups.
Isaak Moiseevich Yaglom deduced complete classification of geometric spaces. In this work, supposed to your attention, author formalizes Yaglom's approach and constructs uniform theory of geometric spaces on analytic level. Among its…
We relate the notions of spectral gap for unitary representations and subfactors with definability of certain important sets in the corresponding structures. We give several applications of this relationship.
We introduce a (bi)category $\mathfrak{Sing}$ whose objects can be functorially assigned spaces of distributions and generalized functions. In addition, these spaces of distributions and generalized functions possess intrinsic notions of…
Powerspaces of directed spaces play an important role in modeling the semantics of nondeterministic functional programming languages. The notions of upper,lower and convex powerspace of a directed space are defined by the way of free…
We give a comprehensive representation of the construction of dyadic cubes in spaces of homogeneous type.
We develop a representation theory of categories as a means to explore characteristic structures in algebra. Characteristic structures play a critical role in isomorphism testing of groups and algebras, and their construction and…
A `discrete differential manifold' we call a countable set together with an algebraic differential calculus on it. This structure has already been explored in previous work and provides us with a convenient framework for the formulation of…
Given an ideal $I$ in a commutative ring $A$, a divided power structure on $I$ is a collection of maps $\{\gamma_n \colon I \to A\}_{n \in \mathbb{N}}$, subject to axioms that imply that it behaves like the family $\{x \mapsto…
We provide a new representation of a refinable shift invariant space with a compactly supported generator, in terms of functions with a special property of homogeneity. In particular these functions include all the homogeneous polynomials…
The existence of invariant generators for distributions satisfying a compatibility condition with the symmetry algebra is proved.