TL;DR
This paper proves Yosida duality, establishing a dual equivalence between the category of compact Hausdorff spaces and the category of uniformly complete Archimedean Riesz spaces with units.
Contribution
It provides a formal proof of Yosida duality, connecting topological spaces with algebraic Riesz spaces in a categorical framework.
Findings
Category of compact Hausdorff spaces is dually equivalent to Riesz spaces with units
Establishes a duality functor between the two categories
Clarifies the structure-preserving maps in the duality
Abstract
In this note we prove Yosida duality --- that is: the category of compact Hausdorff spaces with continuous maps is dually equivalent to the category of uniformly complete Archimedean Riesz spaces with distinguished units and unit-preserving Riesz homomorphisms between them.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Homotopy and Cohomology in Algebraic Topology · Advanced Banach Space Theory