Hereditary D-property of function spaces over compacta

Buzyakova, Raushan

doi:10.1090/S0002-9939-04-07472-6

Hereditary D-property of function spaces over compacta
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by Raushan Z. Buzyakova PDF

Proc. Amer. Math. Soc. 132 (2004), 3433-3439 Request permission

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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