Concrete description of CD0(K)-spaces as C(X)-spaces and its applications

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2004-01-01

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Ercan, Z

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We prove that for a compact Hausdorff space K without isolated points, CD0(K) and C(K x {0, 1}) are isometrically Riesz isomorphic spaces under a certain topology on K x {0, 1}. Moreover, K is a closed subspace of K x {0, 1}. This provides concrete examples of compact Hausdorff spaces X such that the Dedekind completion of C(X) is B(S) (= the set of all bounded real-valued functions on S) since the Dedekind completion of CD0(K) is B(K) (CD0(K, E) and CDw (K, E) spaces as Banach lattices).

Subject Keywords

Applied Mathematics, General Mathematics

URI

https://hdl.handle.net/11511/63630

Journal

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

DOI

https://doi.org/10.1090/s0002-9939-03-07235-6

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Department of Mathematics, Article

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Citation Formats

Z. Ercan, “Concrete description of CD0(K)-spaces as C(X)-spaces and its applications,” PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, pp. 1761–1763, 2004, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/63630.