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

• Autores: Z. Ercan, S. Onal
• Localización: Siberian mathematical journal, ISSN 0037-4466, Vol. 48, Nº. 2, 2007, págs. 382-384
• Idioma: inglés
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• Resumen

  • 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.