## Raushan Z. Buzyakova

*In search for Lindel\"of $C_p$'s *

Comment.Math.Univ.Carolinae 45,1 (2004) 145-151. **Abstract:**It is shown that if $X$ is a first-countable countably compact subspace of ordinals then $C_p(X)$ is Lindel\"of. 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 Lindel\"of number of $C_p(X)$. This example answers negatively Reznichenko's question whether Baturov's theorem holds for countably compact spaces.

**Keywords:** $C_p(X)$, space of ordinals, Lindel\"of space

**AMS Subject Classification:** 54C35, 54D20, 54F05

PDF