On the sequential order continuity of the C(K)-space
SIBERIAN MATHEMATICAL JOURNAL, vol.48, no.2, pp.382-384, 2007 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 48 Issue: 2
- Publication Date: 2007
- Doi Number: 10.1007/s11202-007-0040-2
- Journal Name: SIBERIAN MATHEMATICAL JOURNAL
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.382-384
- Middle East Technical University Affiliated: No
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.