摘要
Let {E<sub>i</sub>:i∈I}be a family of Archimedean Riesz spaces.The Riesz product space is denoted by Π<sub>i∈I</sub> E<sub>i</sub>.The main result in this paper is the following conclusion:There exists a completely regular Hausdorff space X such that Π<sub>i∈I</sub> E<sub>i</sub> is Riesz isomorphic to C（X）if and only if for every i ∈ I there exists a completely regular Hausdorff space X<sub>i</sub> such that E<sub>i</sub> is Riesz isomorphic to C（X<sub>i</sub>）.
Let {E<sub>i</sub>:i∈I}be a family of Archimedean Riesz spaces.The Riesz product space is denoted by Π<sub>i∈I</sub> E<sub>i</sub>.The main result in this paper is the following conclusion:There exists a completely regular Hausdorff space X such that Π<sub>i∈I</sub> E<sub>i</sub> is Riesz isomorphic to C（X）if and only if for every i ∈ I there exists a completely regular Hausdorff space X<sub>i</sub> such that E<sub>i</sub> is Riesz isomorphic to C（X<sub>i</sub>）.
基金
Supported by the National Natural Science Foundation of China
