Let X 1, X 2,â¦, X n be realcompact spaces and Z be a topological space. Let Ï:C(X 1) Ã C(X 2) Ã ··· Ã C(X n ) â C(Z) be a Riesz n-morphism. We show that there exist functions Ï i : Z â X i (i = 1, 2,â¦, n) and w  C(Z) such that and Ï1, Ï2,â¦, Ï n are continuous on {z : w(z) â  0}. This fact extends a result in Boulabiar (20024. Boulabiar , K. ( 2002 ). Some aspects of Riesz multimorphisms . Indag. Math. 13 ( 4 ): 419 - 432 .[CrossRef], [Web of Science ®]View all references) and leads to one of the main results in Boulabiar (20045. Boulabiar , K. ( 2004 ). Representation theorems for d-multiplications on Archimedean unital f-rings . Comm. Algebra 32 ( 10 ): 3955 - 3967 .[Taylor & Francis Online], [Web of Science ®]View all references) with a more elementary proof.View full textDownload full textKey Words f-algebras, Realcompact space, Riesz n-morphism2000 Mathematics Subject ClassificationPrimary 46E25, 06F25Related var addthis_config = { ui_cobrand: "Taylor & Francis Online", services_compact: "citeulike,netvibes,twitter,technorati,delicious,linkedin,facebook,stumbleupon,digg,google,more", pubid: "ra-4dff56cd6bb1830b" }; Add to shortlist Link Permalink http://dx.doi.org/10.1080/00927870701776946
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机译：令X 1 ，X 2 ，…，X n 是实紧空间，Z是拓扑空间。令Ï€：C（X 1 ）Ã-C（X 2 ）Ã-····Ã-C（X < sub> n ）→C（Z）是Riesz n态。我们证明存在函数σ i ：Z→X i （i = 1，2 ,,€，n）和w C（ Z）使得σ 1 ，σ 2 ，â，σ n 在{z：w（z ）≥0}。这一事实扩展了Boulabiar（20024. Boulabiar，K.（2002）。Riesz多态的某些方面。Indag。Math。13（4）：419-432。[CrossRef]，[Web of Science®]查看所有参考）并得出Boulabiar（20045. Boulabiar，K.（2004）。在Archimedean f f环上d乘积的表示定理。Comm。Algebra 32（10）：3955-3967。[Taylor＆弗朗西斯在线]，[Web of Science®]查看所有参考文献），具有更基本的证明。泰勒和弗朗西斯在线”，services_compact：“ citeulike，netvibes，twitter，technorati，delicious，linkedin，facebook，stumbleupon，digg，google，更多”，发布号：“ ra-4dff56cd6bb1830b”};添加到候选列表链接永久链接http://dx.doi.org/10.1080/00927870701776946
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