Oleg Okunev
On the Lindel\"of property of spaces of continuous functions over a Tychonoff space and its subspaces

Comment.Math.Univ.Carolin. 50,4 (2009) 629-635.

Abstract:We study relations between the Lindel\"of property in the spaces of continuous functions with the topology of pointwise convergence over a Tychonoff space and over its subspaces. We prove, in particular, the following: a) if $C_p(X)$ is Lindel\"of, $Y=X\cup\{p\}$, and the point $p$ has countable character in $Y$, then $C_p(Y)$ is Lindel\"of; b) if $Y$ is a cozero subspace of a Tychonoff space $X$, then $l(C_p(Y)^\omega)\le l(C_p(X)^\omega)$ and $\operatorname{ext}(C_p(Y)^\omega)\le \operatorname{ext}(C_p(X)^\omega)$.

Keywords: pointwise convergence, Lindel\"of property
AMS Subject Classification: 54C35 54D20