Data di Pubblicazione:
2014
Citazione:
Unital hyperarchimedean vector lattices / R. N. Ball, V. Marra. - In: TOPOLOGY AND ITS APPLICATIONS. - ISSN 0166-8641. - 170(2014 Jun 15), pp. 10-24.
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.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Archimedean property; Boolean algebra; Boolean space; Cantor space; Hyperarchimedean property; Lattice-ordered group; Locally constant function; Prime spectrum; Ring of continuous functions; Stone space; Strong order unit; Vector lattice; Weak order unit; Yosida representation
Elenco autori:
R. N. Ball, V. Marra
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