On weakly compact sets in $$C\left( X\right) $$

A subset of a locally convex space E is called (relatively) sequentially complete if every Cauchy sequence $$\left\{ x_{n}\right\} _{n=1}^{\infty }$$ in contained converges to point $$x\in A$$ (a E$$ ). Asanov and Velichko proved that X countably compact, functionally bounded set $$C_{p}\left( X\right) $$ relatively Baturov showed Lindelöf $$\Sigma -space, each compact (so bounded) C_{p}\left( monolithic compact. We show or $$C_{w}\left( , i. e., $$C_{k}\left( equipped with the weak topology, Gul’ko get some consequences.