Duality Between Uniform Spaces and Boolean Algebras
Joseph Van Name
TL;DR
This paper extends Stone duality to encompass all complete non-Archimedean uniform spaces and Boolean algebras, broadening the classical correspondence beyond compact totally disconnected spaces.
Contribution
It introduces a duality framework connecting complete non-Archimedean uniform spaces with Boolean algebras, generalizing existing Stone duality.
Findings
Establishes a duality between complete non-Archimedean uniform spaces and Boolean algebras.
Generalizes classical Stone duality beyond compact totally disconnected spaces.
Provides a new perspective on the structure of uniform spaces and Boolean algebras.
Abstract
In this note we shall generalize the Stone duality between compact totally disconnected spaces and Boolean algebras to a duality between all complete non-Archimedean uniform spaces and Boolean algebras.
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Taxonomy
TopicsAdvanced Topology and Set Theory