The Stone's Representation Theorems and compactifications of a discrete space
Hussain Rashed
TL;DR
This paper explains Stone's Representation Theorems through three approaches and applies them to analyze compactifications of discrete spaces, linking algebraic and topological perspectives.
Contribution
It offers three equivalent methods to construct Stone's spaces from Boolean algebras and demonstrates their use in studying compactifications of discrete spaces.
Findings
Three equivalent constructions of Stone's spaces from Boolean algebras
Application of Stone's Theorems to compactifications of discrete spaces
Bridging algebraic and topological methods in space analysis
Abstract
This paper is meant to give a short exposition of the Stone's Representation Theorems. We provide three equivalent approaches to construct a Stone's space from a given Boolean algebra. Finally, we utilize the Stone's Representation Theorems to study the compactifications of a discrete space.
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Taxonomy
TopicsDigital Image Processing Techniques · Advanced Algebra and Logic · Advanced Topology and Set Theory