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Hereditary D-property of function spaces over compacta


Author: Raushan Z. Buzyakova
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
Published electronically: May 20, 2004
MathSciNet review: 2073321
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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 Matveev's question. A connection between the $D$-property and Baturov's and Grothendieck's classical theorems about function spaces over compacta is established.

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Additional Information

Raushan Z. Buzyakova
Affiliation: Department of Mathematics, Brooklyn College, Brooklyn, New York 11210
Email: RaushanB@brooklyn.cuny.edu

DOI: https://doi.org/10.1090/S0002-9939-04-07472-6
Keywords: $C_p(X)$, $D$-space
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 author’s research was supported by PSC-CUNY grant 64457-00 33.
Dedicated: To my teacher Alexander Arhangel’skii for his $65^{th}$ birthday
Communicated by: Alan Dow
Article copyright: © Copyright 2004 American Mathematical Society