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


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Ercan Z.

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, vol.132, no.6, pp.1761-1763, 2004 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 132 Issue: 6
  • Publication Date: 2004
  • Doi Number: 10.1090/s0002-9939-03-07235-6
  • Journal Name: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.1761-1763

Abstract

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).