Does the network of $X$ equal to the network of $C\_p(X)$?


$C\_p(X)$ denotes the set of all real-valued continuous functions on $X$ endowed with the topology of pointwise convergence.


Thanks!



Does the network of $X$ equal to the network of $C_p(X)$?
The following is Theorem I.1.3 in *Topological Function Spaces* by A.V. Arkhangelski:



> 
> For any space $X$, $nw(X)=nw(C\_p(X))$.
> 
> 
> 


Where $nw(X)$ denotes the network weight of $X$ (i.e. the minimal cardinality of a network in $X$).


