Hereditary D-property of function spaces over compacta
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- by Raushan Z. Buzyakova
- Proc. Amer. Math. Soc. 132 (2004), 3433-3439
- DOI: https://doi.org/10.1090/S0002-9939-04-07472-6
- Published electronically: May 20, 2004
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Abstract:
It is shown that if $X$ is compact then every subspace of $C_p(X)$ is a $D$-space in the sense of E. van Douwen, which positively answers Matveevās question. A connection between the $D$-property and Baturovās and Grothendieckās classical theorems about function spaces over compacta is established.References
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Bibliographic Information
- Raushan Z. Buzyakova
- Affiliation: Department of Mathematics, Brooklyn College, Brooklyn, New York 11210
- Email: RaushanB@brooklyn.cuny.edu
- Received by editor(s): April 21, 2003
- Received by editor(s) in revised form: July 31, 2003
- Published electronically: May 20, 2004
- Additional Notes: The authorās research was supported by PSC-CUNY grant 64457-00 33.
- Communicated by: Alan Dow
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 3433-3439
- MSC (2000): Primary 54C35, 54D20, 54C60
- DOI: https://doi.org/10.1090/S0002-9939-04-07472-6
- MathSciNet review: 2073321
Dedicated: To my teacher Alexander Arhangelāskii for his $65^{\textit {th}}$ birthday