A New Proof on Embedding the Category of Proximity Spaces into the Category of Nearness Spaces

Authors:
Zhanbo Yang
Affiliations:
(Correspd.) Department of Mathematics, University of the Incarnate Word, 4301 Broadway, San Antonio, TX 78209, USA. yang@uiwtx.edu
Venue:
Fundamenta Informaticae
Year:
2008

Citing 7
Cited 0

Abstract and concrete categories

Abstract and concrete categories
Semi-proximity continuous functions in digital images

Pattern Recognition Letters
A new definition of neighborhood of a point in multi-dimensional space

Pattern Recognition Letters
Rough Sets: Theoretical Aspects of Reasoning about Data

Rough Sets: Theoretical Aspects of Reasoning about Data
Nearness in Digital Images and Proximity Spaces

DGCI '00 Proceedings of the 9th International Conference on Discrete Geometry for Computer Imagery
Nearness of Objects: Extension of Approximation Space Model

Fundamenta Informaticae - Special Issue on Concurrency Specification and Programming (CS&P)
Approximation Spaces and Nearness Type Structures

Fundamenta Informaticae - Special Issue on Concurrency Specification and Programming (CS&P)

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper establishes an explicit embedding functor from the category of the proximity spaces into the category of nearness spaces. This is done by defining methods to constructively inducing a proximity structure with a given nearness structure and vis versa. Those induction methods provide useful tools to understand the inter-relations and to translate the result between the two types of spaces.