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Paper IPM / M / 16011  


Abstract:  
In this paper, we study the local ordered ï¿½??vector spaces and their representations. We prove that each Archimedean local orderedï¿½??vector space, can be represented as a ï¿½??vector subspace of C(X), for some completely Hausdorï¿½? compactly generated space X. Furthermore, we show that for every Archimedean local ordered ï¿½??vector space V , there is a representation of V into the ï¿½??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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