Geodesic
In search for Lindelöf $C_p$'s
Commentationes Mathematicae Universitatis Carolinae, Tome 45 (2004) no. 1, pp. 145-151.

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It is shown that if $X$ is a first-countable countably compact subspace of ordinals then $C_p(X)$ is Lindelöf. This result is used to construct an example of a countably compact space $X$ such that the extent of $C_p(X)$ is less than the Lindelöf number of $C_p(X)$. This example answers negatively Reznichenko's question whether Baturov's theorem holds for countably compact spaces.
Classification : 54C35, 54D20, 54F05
Keywords: $C_p(X)$; space of ordinals; Lindelöf space 
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Buzyakova, Raushan Z. In search for Lindelöf $C_p$'s. Commentationes Mathematicae Universitatis Carolinae, Tome 45 (2004) no. 1, pp. 145-151. http://geodesic.mathdoc.fr/item/CMUC_2004__45_1_a10/