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.
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Original Russian Text Copyright © 2007 Ercan Z. and Önal S.
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 48, No. 2, pp. 474–477, March–April, 2007.
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Ercan, Z., Önal, S. On the sequential order continuity of the C(K)-space. Sib Math J 48, 382–384 (2007). https://doi.org/10.1007/s11202-007-0040-2
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DOI: https://doi.org/10.1007/s11202-007-0040-2