A new representation of the Dedekind completion of C(K)-spaces

A new representation of the Dedekind completion of C(K) is given. We present a necessary and sufficient condition on a compact Hausdorff space K for which the Dedekind completion of C(K) is B(S), the space of real valued bounded functions on some set S.

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2005-11, Vol.133 (11), p.3317-3321
Main Authors: ERCAN, Z, ONAL, S
Format: Article
Language:English
Subjects:
Completely Hausdorff spaces
Exact sciences and technology
Functional analysis
General topology
Hausdorff spaces
Mathematical analysis
Mathematical functions
Mathematical lattices
Mathematical theorems
Mathematics
Real numbers
Sciences and techniques of general use
Topological spaces
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Urelements
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Description
Summary:A new representation of the Dedekind completion of C(K) is given. We present a necessary and sufficient condition on a compact Hausdorff space K for which the Dedekind completion of C(K) is B(S), the space of real valued bounded functions on some set S.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-05-07889-5