Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Finitary approximations of coarse structures
View through CrossRef
A coarse structure $ \mathcal{E}$ on a set $X$ is called finitary if, for each entourage $E\in \mathcal{E}$, there exists a natural number $n$ such that $ E[x]< n $ for each $x\in X$. By a finitary approximation of a coarse structure $ \mathcal{E}^\prime$, we mean any finitary coarse structure $ \mathcal{E}$ such that $ \mathcal{E}\subseteq \mathcal{E}^\prime$.If $\mathcal{E}^\prime$ has a countable base and $E[x]$ is finite for each $x\in X$ then $ \mathcal{E}^\prime$has a cellular finitary approximation $ \mathcal{E}$ such that the relations of linkness on subsets of $( X,\mathcal{E}^\prime)$ and $( X, \mathcal{E})$ coincide.This answers Question 6 from [8]: the class of cellular coarse spaces is not stable under linkness. We define and apply the strongest finitary approximation of a coarse structure.
Title: Finitary approximations of coarse structures
Description:
A coarse structure $ \mathcal{E}$ on a set $X$ is called finitary if, for each entourage $E\in \mathcal{E}$, there exists a natural number $n$ such that $ E[x]< n $ for each $x\in X$.
By a finitary approximation of a coarse structure $ \mathcal{E}^\prime$, we mean any finitary coarse structure $ \mathcal{E}$ such that $ \mathcal{E}\subseteq \mathcal{E}^\prime$.
If $\mathcal{E}^\prime$ has a countable base and $E[x]$ is finite for each $x\in X$ then $ \mathcal{E}^\prime$has a cellular finitary approximation $ \mathcal{E}$ such that the relations of linkness on subsets of $( X,\mathcal{E}^\prime)$ and $( X, \mathcal{E})$ coincide.
This answers Question 6 from [8]: the class of cellular coarse spaces is not stable under linkness.
We define and apply the strongest finitary approximation of a coarse structure.
Related Results
Algebras of finitary relations
Algebras of finitary relations
Algebras of finitary relations naturally generalize the algebra of binary relations with the left composition. In this paper, we consider some properties of such algebras. It is we...
Analytical and Numerical Approximations to Some Coupled Forced Damped Duffing Oscillators
Analytical and Numerical Approximations to Some Coupled Forced Damped Duffing Oscillators
In this investigation, two different models for two coupled asymmetrical oscillators, known as, coupled forced damped Duffing oscillators (FDDOs) are reported. The first model of c...
Making the Case for the Use of Effective Tension in Casing Design to Eliminate Approximations and Wall Thickness Limitations
Making the Case for the Use of Effective Tension in Casing Design to Eliminate Approximations and Wall Thickness Limitations
Abstract
Existing plastic limit load equations for casing design include approximations that can result in overly conservative (and costly) well designs and ignore f...
On asymorphisms of finitary coarse spaces
On asymorphisms of finitary coarse spaces
We characterize finitary coarse spaces X such that every permutation of X is an asymorphism....
Unstructured-Coarse-Grid Generation Using Background-Grid Approach
Unstructured-Coarse-Grid Generation Using Background-Grid Approach
Summary
Reservoir flow simulation involves subdivision of the physical domain into a number of gridblocks. This is best accomplished with optimized gridpoint density...
Unstructured Coarse Grid Generation for Reservoir Flow Simulation Using Background Grid Approach
Unstructured Coarse Grid Generation for Reservoir Flow Simulation Using Background Grid Approach
Abstract
Reservoir flow simulation involves subdivision of the physical domain into a number of gridblocks. This is best accomplished with optimized grid point densi...
MECHANICAL PROPERTIES OF CONCRETE BY ADDING PLASTIC AS A PARTIAL SUBSTITUTE FOR COARSE AGGREGATE TO PROMOTE SUSTAINABILITY ON CONSTRUCTION INDUSTRY
MECHANICAL PROPERTIES OF CONCRETE BY ADDING PLASTIC AS A PARTIAL SUBSTITUTE FOR COARSE AGGREGATE TO PROMOTE SUSTAINABILITY ON CONSTRUCTION INDUSTRY
Concrete is without a doubt the most advantageous material in the building industry, but every coin has two sides. Raw materials used in the manufacturing of concrete, in one way o...
Effect of Coarse Content on Compaction Test
Effect of Coarse Content on Compaction Test
The compaction is a mechanism to densify the loose soils. The maximum soil densification can be achieved by optimization of the desirable optimum moisture content (OMC) and maximum...