On the sequential order continuity of the <Emphasis Type="Italic">C</Emphasis>(<Emphasis Type="Italic">K</Emphasis>)-space |
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Authors: | Z Ercan S Önal |
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Institution: | (1) Middle East Technical University, Ankara, Turkey |
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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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Keywords: | F-space P′ -space Cantor property sequentially order continuous norm isometrically Riesz isomorphism |
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