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| Paper IPM / M / 16011 |
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| Abstract: | |
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In this paper, we study the local ordered �??-vector spaces and their representations. We prove that each Archimedean local ordered�??-vector space, can be represented as a �??-vector subspace of C(X), for some completely Hausdor�? compactly generated space X. Furthermore, we show that for every Archimedean local ordered �??-vector space V , there is a representation of V into the �??-algebra of all noncommutative continuous functions on a quantum domain E such that the quantum order induced by this representation is the minimal quantum system structure on V .
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