Proximal and Descriptive Topological Rings: Structure and Properties

2025/09/01 by Almahariq, Maram
#22A20 #54E05 #54E17 #54H05 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.01466

Abstract

The set of open subsets in a proximity space (X,ζ) forms a topological system that enables the definition of proximal and descriptive topological groups. This framework naturally extends to proximal and descriptive topological rings as well. In this study, I review fundamental properties and related results, with particular emphasis on the definition of proximal and descriptive fields. In addition, I examine the behavior of closed sets in proximal and descriptive topological rings.

Citations

• Topological Group Construction In Proximity And Descriptive Proximity Spaces
• Good Coverings of Proximal Alexandrov Spaces. Path Cycles in the Extension of the Mitsuishi-Yamaguchi good covering and Jordan Curve Theorems
• Descriptive Fixed Set Properties for Ribbon Complexes
• Descriptive Proximities I: Properties and interplay between classical proximities and overlap
• Strongly Proximal Continuity & Strong Connectedness

Related

• Topological Group Construction In Proximity And Descriptive Proximity Spaces
• Descriptive Proximities I: Properties and interplay between classical proximities and overlap
• Descriptive Fixed Set Properties for Ribbon Complexes
• Geometrically closed rings
• On relationships between algebraic properties of groups and rings in some model-theoretic contexts