A Characterization of Riesz n-Morphisms and Applications

Let X 1 , X 2 ,..., X n be realcompact spaces and Z be a topological space. Let π:C(X 1 ) × C(X 2 ) × ··· × C(X n ) → C(Z) be a Riesz n-morphism. We show that there exist functions σ i : Z → X i (i = 1, 2,..., n) and w ∈ C(Z) such that and σ 1 , σ 2 ,..., σ n are continuous on {z : w(z) ≠ 0}. This f...

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Bibliographic Details
Published in:Communications in algebra 2008-03, Vol.36 (3), p.1115-1120
Main Authors: Ercan, Z., Önal, S.
Format: Article
Language:English
Subjects:
f-algebras
Primary 46E25, 06F25
Realcompact space
Riesz n-morphism
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Summary:Let X 1 , X 2 ,..., X n be realcompact spaces and Z be a topological space. Let π:C(X 1 ) × C(X 2 ) × ··· × C(X n ) → C(Z) be a Riesz n-morphism. We show that there exist functions σ i : Z → X i (i = 1, 2,..., n) and w ∈ C(Z) such that and σ 1 , σ 2 ,..., σ n are continuous on {z : w(z) ≠ 0}. This fact extends a result in Boulabiar ( 2002 ) and leads to one of the main results in Boulabiar ( 2004 ) with a more elementary proof.
ISSN:0092-7872
1532-4125
DOI:10.1080/00927870701776946