On the sequential order continuity of the C(K)-space


Ercan Z., Onal S.

SIBERIAN MATHEMATICAL JOURNAL, vol.48, no.2, pp.382-384, 2007 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 48 Issue: 2
  • Publication Date: 2007
  • Doi Number: 10.1007/s11202-007-0040-2
  • Title of Journal : SIBERIAN MATHEMATICAL JOURNAL
  • Page Numbers: pp.382-384

Abstract

As shown in [1], for each compact Hausdorff space K without isolated points, there exists a compact Hausdorff P'-space X but not an F-space such that C(K) is isometrically Riesz isomorphic to a Riesz subspace of C(X). The proof is technical and depends heavily on some representation theorems. In this paper we give a simple and direct proof without any assumptions on isolated points. Some generalizations of these results are mentioned.