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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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Published in: | Communications in algebra 2008-03, Vol.36 (3), p.1115-1120 |
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Main Authors: | , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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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. |
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ISSN: | 0092-7872 1532-4125 |
DOI: | 10.1080/00927870701776946 |