Abstract
Let {E i:i∈I} be a family of Archimedean Riesz spaces. The Riesz product space is denoted by ∏ i∈I Ei. The main result in this paper is the following conclusion: There exists a completely regular Hausdorff spaceX such that ∏ i∈I Ei is Riesz isomorphic toC(X) if and only if for everyi∈I there exists a completely regular Hausdorff spaceX i such thatE i is Riesz isomorphic toC(X i).
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Supported by the National Natural Science Foundation of China
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Hongyun, X., Ximin, R. Riesz product spaces and representation theory. Acta Mathematica Sinica 14, 169–174 (1998). https://doi.org/10.1007/BF02560203
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DOI: https://doi.org/10.1007/BF02560203