We prove that the category of unital hyperarchimedean vector lattices is equivalent to the category of Boolean algebras. The key result needed to establish the equivalence is that, via the Yosida representation, such a vector lattice is naturally isomorphic to the vector lattice of all locally constant real-valued continuous functions on a Boolean (= compact Hausdorff totally disconnected) space. We give two applications of our main result.
Unital hyperarchimedean vector lattices / R. N. Ball, V. Marra. - In: TOPOLOGY AND ITS APPLICATIONS. - ISSN 0166-8641. - 170(2014 Jun 15), pp. 10-24.
Unital hyperarchimedean vector lattices
V. Marra
2014
Abstract
We prove that the category of unital hyperarchimedean vector lattices is equivalent to the category of Boolean algebras. The key result needed to establish the equivalence is that, via the Yosida representation, such a vector lattice is naturally isomorphic to the vector lattice of all locally constant real-valued continuous functions on a Boolean (= compact Hausdorff totally disconnected) space. We give two applications of our main result.
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