A Unified Approach to Gelfand and de Vries Dualities
Guram Bezhanishvili, Luca Carai, Patrick Morandi, Bruce Olberding
TL;DR
This paper presents a unified framework connecting Gelfand and de Vries dualities for compact Hausdorff spaces, integrating classical results from analysis, lattice theory, and topology.
Contribution
It introduces a novel unified approach that bridges Gelfand and de Vries dualities through modifications of classical theorems.
Findings
Unified duality framework for compact Hausdorff spaces
Connections established between analysis, lattice theory, and topology
Enhanced understanding of duality principles in topology
Abstract
We develop a unified approach to Gelfand and de Vries dualities for compact Hausdorff spaces, which is based on appropriate modifications of the classic results of Dieudonn\'{e} (analysis), Dilworth (lattice theory), and Kat{\v{e}}tov-Tong (topology).
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Taxonomy
TopicsAdvanced Topology and Set Theory · Advanced Banach Space Theory · Rings, Modules, and Algebras