On the sequential order continuity of the C(K)-space
SIBERIAN MATHEMATICAL JOURNAL, cilt.48, sa.2, ss.382-384, 2007 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 48 Sayı: 2
- Basım Tarihi: 2007
- Doi Numarası: 10.1007/s11202-007-0040-2
- Dergi Adı: SIBERIAN MATHEMATICAL JOURNAL
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.382-384
- Orta Doğu Teknik Üniversitesi Adresli: Hayır
Özet
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.