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


Ercan Z., Onal S.

SIBERIAN MATHEMATICAL JOURNAL, cilt.48, ss.382-384, 2007 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 48 Konu: 2
  • Basım Tarihi: 2007
  • Doi Numarası: 10.1007/s11202-007-0040-2
  • Dergi Adı: SIBERIAN MATHEMATICAL JOURNAL
  • Sayfa Sayıları: ss.382-384

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.